prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How is electricity used in everyday life?

Read the following text and answer briefly.

Context 1: For other uses, see Electricity (disambiguation) 
"Electric" redirects here  For other uses, see Electric (disambiguation) 
Lightning is one of the most dramatic effects of electricity 
Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge  In early days, electricity was considered as being not related to magnetism  Later on, many experimental results and the development of Maxwell's equations indicated that both electricity and magnetism are from a single phenomenon: electromagnetism  Various common phenomena are related to electricity, including lightning, static electricity, electric heating, electric discharges and many others 
The presence of an electric charge, which can be either positive or negative, produces an electric field  The movement of electric charges is an electric current and produces a magnetic field 
When a charge is placed in a location with a non-zero electric field, a force will act on it  The magnitude of this force is given by Coulomb's law  Thus, if that charge were to move, the electric field would be doing work on the electric charge  Thus we can speak of electric potential at a certain point in space, which is equal to the work done by an external agent in carrying a unit of positive charge from an arbitrarily chosen reference point to that point without any acceleration and is typically measured in volts 
electronics which deals with electrical circuits that involve active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies 
Electrical phenomena have been studied since antiquity, though progress in theoretical understanding remained slow until the seventeenth and eighteenth centuries  Even then, practical applications for electricity were few, and it would not be until the late nineteenth century that electrical engineers were able to put it to industrial and residential use  The rapid expansion in electrical technology at this time transformed industry and society, becoming a driving force for the Second Industrial Revolution  Electricity's extraordinary versatility means it can be put to an almost limitless set of applications which include transport, heating, lighting, communications, and computation  Electrical power is now the backbone of modern industrial society 
Long before any knowledge of electricity existed, people were aware of shocks from electric fish  Ancient Egyptian texts dating from 2750 BCE referred to these fish as the "Thunderer of the Nile", and described them as the "protectors" of all other fish  Electric fish were again reported millennia later by ancient Greek, Roman and Arabic naturalists and physicians  Several ancient writers, such as Pliny the Elder and Scribonius Largus, attested to the numbing effect of electric shocks delivered by catfish and electric rays, and knew that such shocks could travel along conducting objects  Patients suffering from ailments such as gout or headache were directed to touch electric fish in the hope that the powerful jolt might cure them  Possibly the earliest and nearest approach to the discovery of the identity of lightning, and electricity from any other source, is to be attributed to the Arabs, who before the 15th century had the Arabic word for lightning ra‘ad (رعد) applied to the electric ray 
Ancient cultures around the Mediterranean knew that certain objects, such as rods of amber, could be rubbed with cat's fur to attract light objects like feathers  Thales of Miletus made a series of observations on static electricity around 600 BCE, from which he believed that friction rendered amber magnetic, in contrast to minerals such as magnetite, which needed no rubbing  Thales was incorrect in believing the attraction was due to a magnetic effect, but later science would prove a link between magnetism and electricity  According to a controversial theory, the Parthians may have had knowledge of electroplating, based on the 1936 discovery of the Baghdad Battery, which resembles a galvanic cell, though it is uncertain whether the artifact was electrical in nature 
Benjamin Franklin conducted extensive research on electricity in the 18th century, as documented by Joseph Priestley (1767) History and Present Status of Electricity, with whom Franklin carried on extended correspondence 
Electricity would remain little more than an intellectual curiosity for millennia until 1600, when the English scientist William Gilbert wrote De Magnete, in which he made a careful study of electricity and magnetism, distinguishing the lodestone effect from static electricity produced by rubbing amber  He coined the New Latin word electricus ("of amber" or "like amber", from ἤλεκτρον, elektron, the Greek word for "amber") to refer to the property of attracting small objects after being rubbed  This association gave rise to the English words "electric" and "electricity", which made their first appearance in print in Thomas Browne's Pseudodoxia Epidemica of 1646 
Further work was conducted in the 17th and early 18th centuries by Otto von Guericke, Robert Boyle, Stephen Gray and C  F  du Fay  Later in the 18th century, Benjamin Franklin conducted extensive research in electricity, selling his possessions to fund his work  In June 1752 he is reputed to have attached a metal key to the bottom of a dampened kite string and flown the kite in a storm-threatened sky  A succession of sparks jumping from the key to the back of his hand showed that lightning was indeed electrical in nature  He also explained the apparently paradoxical behavior of the Leyden jar as a device for storing large amounts of electrical charge in terms of electricity consisting of both positive and negative charges 
In 1791, Luigi Galvani published his discovery of bioelectromagnetics, demonstrating that electricity was the medium by which neurons passed signals to the muscles  Alessandro Volta's battery, or voltaic pile, of 1800, made from alternating layers of zinc and copper, provided scientists with a more reliable source of electrical energy than the electrostatic machines previously used  The recognition of electromagnetism, the unity of electric and magnetic phenomena, is due to Hans Christian Ørsted and André-Marie Ampère in 1819–1820  Michael Faraday invented the electric motor in 1821, and Georg Ohm mathematically analysed the electrical circuit in 1827  Electricity and magnetism (and light) were definitively linked by James Clerk Maxwell, in particular in his "On Physical Lines of Force" in 1861 and 1862 
While the early 19th century had seen rapid progress in electrical science, the late 19th century would see the greatest progress in electrical engineering  Through such people as Alexander Graham Bell, Ottó Bláthy, Thomas Edison, Galileo Ferraris, Oliver Heaviside, Ányos Jedlik, William Thomson, 1st Baron Kelvin, Charles Algernon Parsons, Werner von Siemens, Joseph Swan, Reginald Fessenden, Nikola Tesla and George Westinghouse, electricity turned from a scientific curiosity into an essential tool for modern life 
In 1887, Heinrich Hertz:843–44 discovered that electrodes illuminated with ultraviolet light create electric sparks more easily  In 1905, Albert Einstein published a paper that explained experimental data from the photoelectric effect as being the result of light energy being carried in discrete quantized packets, energising electrons  This discovery led to the quantum revolution  Einstein was awarded the Nobel Prize in Physics in 1921 for "his discovery of the law of the photoelectric effect"  The photoelectric effect is also employed in photocells such as can be found in solar panels and this is frequently used to make electricity commercially 
The first solid-state device was the "cat's-whisker detector" first used in the 1900s in radio receivers  A whisker-like wire is placed lightly in contact with a solid crystal (such as a germanium crystal) to detect a radio signal by the contact junction effect  In a solid-state component, the current is confined to solid elements and compounds engineered specifically to switch and amplify it  Current flow can be understood in two forms: as negatively charged electrons, and as positively charged electron deficiencies called holes  These charges and holes are understood in terms of quantum physics  The building material is most often a crystalline semiconductor 
The solid-state device came into its own with the invention of the transistor in 1947  Common solid-state devices include transistors, microprocessor chips, and RAM  A specialized type of RAM called flash RAM is used in USB flash drives and more recently, solid-state drives to replace mechanically rotating magnetic disc hard disk drives  Solid state devices became prevalent in the 1950s and the 1960s, during the transition from vacuum tubes to semiconductor diodes, transistors, integrated circuit (IC) and the light-emitting diode (LED) 
The presence of charge gives rise to an electrostatic force: charges exert a force on each other, an effect that was known, though not understood, in antiquity :457 A lightweight ball suspended from a string can be charged by touching it with a glass rod that has itself been charged by rubbing with a cloth  If a similar ball is charged by the same glass rod, it is found to repel the first: the charge acts to force the two balls apart  Two balls that are charged with a rubbed amber rod also repel each other  However, if one ball is charged by the glass rod, and the other by an amber rod, the two balls are found to attract each other  These phenomena were investigated in the late eighteenth century by Charles-Augustin de Coulomb, who deduced that charge manifests itself in two opposing forms  This discovery led to the well-known axiom: like-charged objects repel and opposite-charged objects attract 
The force acts on the charged particles themselves, hence charge has a tendency to spread itself as evenly as possible over a conducting surface  The magnitude of the electromagnetic force, whether attractive or repulsive, is given by Coulomb's law, which relates the force to the product of the charges and has an inverse-square relation to the distance between them :35 The electromagnetic force is very strong, second only in strength to the strong interaction, but unlike that force it operates over all distances  In comparison with the much weaker gravitational force, the electromagnetic force pushing two electrons apart is 1042 times that of the gravitational attraction pulling them together 
Study has shown that the origin of charge is from certain types of subatomic particles which have the property of electric charge  Electric charge gives rise to and interacts with the electromagnetic force, one of the four fundamental forces of nature  The most familiar carriers of electrical charge are the electron and proton  Experiment has shown charge to be a conserved quantity, that is, the net charge within an electrically isolated system will always remain constant regardless of any changes taking place within that system  Within the system, charge may be transferred between bodies, either by direct contact, or by passing along a conducting material, such as a wire :2–5 The informal term static electricity refers to the net presence (or 'imbalance') of charge on a body, usually caused when dissimilar materials are rubbed together, transferring charge from one to the other 
The charge on electrons and protons is opposite in sign, hence an amount of charge may be expressed as being either negative or positive  By convention, the charge carried by electrons is deemed negative, and that by protons positive, a custom that originated with the work of Benjamin Franklin  The amount of charge is usually given the symbol Q and expressed in coulombs; each electron carries the same charge of approximately −1 6022×10−19 coulomb  The proton has a charge that is equal and opposite, and thus +1 6022×10−19 coulomb  Charge is possessed not just by matter, but also by antimatter, each antiparticle bearing an equal and opposite charge to its corresponding particle 
The movement of electric charge is known as an electric current, the intensity of which is usually measured in amperes  Current can consist of any moving charged particles; most commonly these are electrons, but any charge in motion constitutes a current  Electric current can flow through some things, electrical conductors, but will not flow through an electrical insulator 
By historical convention, a positive current is defined as having the same direction of flow as any positive charge it contains, or to flow from the most positive part of a circuit to the most negative part  Current defined in this manner is called conventional current  The motion of negatively charged electrons around an electric circuit, one of the most familiar forms of current, is thus deemed positive in the opposite direction to that of the electrons  However, depending on the conditions, an electric current can consist of a flow of charged particles in either direction, or even in both directions at once  The positive-to-negative convention is widely used to simplify this situation 
The process by which electric current passes through a material is termed electrical conduction, and its nature varies with that of the charged particles and the material through which they are travelling  Examples of electric currents include metallic conduction, where electrons flow through a conductor such as metal, and electrolysis, where ions (charged atoms) flow through liquids, or through plasmas such as electrical sparks  While the particles themselves can move quite slowly, sometimes with an average drift velocity only fractions of a millimetre per second,:17 the electric field that drives them itself propagates at close to the speed of light, enabling electrical signals to pass rapidly along wires 
Current causes several observable effects, which historically were the means of recognising its presence  That water could be decomposed by the current from a voltaic pile was discovered by Nicholson and Carlisle in 1800, a process now known as electrolysis  Their work was greatly expanded upon by Michael Faraday in 1833  Current through a resistance causes localised heating, an effect James Prescott Joule studied mathematically in 1840 :23–24 One of the most important discoveries relating to current was made accidentally by Hans Christian Ørsted in 1820, when, while preparing a lecture, he witnessed the current in a wire disturbing the needle of a magnetic compass  He had discovered electromagnetism, a fundamental interaction between electricity and magnetics  The level of electromagnetic emissions generated by electric arcing is high enough to produce electromagnetic interference, which can be detrimental to the workings of adjacent equipment 
In engineering or household applications, current is often described as being either direct current (DC) or alternating current (AC)  These terms refer to how the current varies in time  Direct current, as produced by example from a battery and required by most electronic devices, is a unidirectional flow from the positive part of a circuit to the negative :11 If, as is most common, this flow is carried by electrons, they will be travelling in the opposite direction  Alternating current is any current that reverses direction repeatedly; almost always this takes the form of a sine wave :206–07 Alternating current thus pulses back and forth within a conductor without the charge moving any net distance over time  The time-averaged value of an alternating current is zero, but it delivers energy in first one direction, and then the reverse  Alternating current is affected by electrical properties that are not observed under steady state direct current, such as inductance and capacitance :223–25 These properties however can become important when circuitry is subjected to transients, such as when first energised 
The concept of the electric field was introduced by Michael Faraday  An electric field is created by a charged body in the space that surrounds it, and results in a force exerted on any other charges placed within the field  The electric field acts between two charges in a similar manner to the way that the gravitational field acts between two masses, and like it, extends towards infinity and shows an inverse square relationship with distance  However, there is an important difference  Gravity always acts in attraction, drawing two masses together, while the electric field can result in either attraction or repulsion  Since large bodies such as planets generally carry no net charge, the electric field at a distance is usually zero  Thus gravity is the dominant force at distance in the universe, despite being much weaker 
A hollow conducting body carries all its charge on its outer surface  The field is therefore zero at all places inside the body :88 This is the operating principal of the Faraday cage, a conducting metal shell which isolates its interior from outside electrical effects 
The principles of electrostatics are important when designing items of high-voltage equipment  There is a finite limit to the electric field strength that may be withstood by any medium  Beyond this point, electrical breakdown occurs and an electric arc causes flashover between the charged parts  Air, for example, tends to arc across small gaps at electric field strengths which exceed 30 kV per centimetre  Over larger gaps, its breakdown strength is weaker, perhaps 1 kV per centimetre  The most visible natural occurrence of this is lightning, caused when charge becomes separated in the clouds by rising columns of air, and raises the electric field in the air to greater than it can withstand  The voltage of a large lightning cloud may be as high as 100 MV and have discharge energies as great as 250 kWh 
A pair of AA cells  The + sign indicates the polarity of the potential difference between the battery terminals 
The concept of electric potential is closely linked to that of the electric field  A small charge placed within an electric field experiences a force, and to have brought that charge to that point against the force requires work  The electric potential at any point is defined as the energy required to bring a unit test charge from an infinite distance slowly to that point  It is usually measured in volts, and one volt is the potential for which one joule of work must be expended to bring a charge of one coulomb from infinity :494–98 This definition of potential, while formal, has little practical application, and a more useful concept is that of electric potential difference, and is the energy required to move a unit charge between two specified points  An electric field has the special property that it is conservative, which means that the path taken by the test charge is irrelevant: all paths between two specified points expend the same energy, and thus a unique value for potential difference may be stated :494–98 The volt is so strongly identified as the unit of choice for measurement and description of electric potential difference that the term voltage sees greater everyday usage 
For practical purposes, it is useful to define a common reference point to which potentials may be expressed and compared  While this could be at infinity, a much more useful reference is the Earth itself, which is assumed to be at the same potential everywhere  This reference point naturally takes the name earth or ground  Earth is assumed to be an infinite source of equal amounts of positive and negative charge, and is therefore electrically uncharged—and unchargeable 
Electric potential is a scalar quantity, that is, it has only magnitude and not direction  It may be viewed as analogous to height: just as a released object will fall through a difference in heights caused by a gravitational field, so a charge will 'fall' across the voltage caused by an electric field  As relief maps show contour lines marking points of equal height, a set of lines marking points of equal potential (known as equipotentials) may be drawn around an electrostatically charged object  The equipotentials cross all lines of force at right angles  They must also lie parallel to a conductor's surface, otherwise this would produce a force that will move the charge carriers to even the potential of the surface 
Ørsted's discovery in 1821 that a magnetic field existed around all sides of a wire carrying an electric current indicated that there was a direct relationship between electricity and magnetism  Moreover, the interaction seemed different from gravitational and electrostatic forces, the two forces of nature then known  The force on the compass needle did not direct it to or away from the current-carrying wire, but acted at right angles to it  Ørsted's slightly obscure words were that "the electric conflict acts in a revolving manner " The force also depended on the direction of the current, for if the flow was reversed, then the force did too 
Ørsted did not fully understand his discovery, but he observed the effect was reciprocal: a current exerts a force on a magnet, and a magnetic field exerts a force on a current  The phenomenon was further investigated by Ampère, who discovered that two parallel current-carrying wires exerted a force upon each other: two wires conducting currents in the same direction are attracted to each other, while wires containing currents in opposite directions are forced apart  The interaction is mediated by the magnetic field each current produces and forms the basis for the international definition of the ampere 
This relationship between magnetic fields and currents is extremely important, for it led to Michael Faraday's invention of the electric motor in 1821  Faraday's homopolar motor consisted of a permanent magnet sitting in a pool of mercury  A current was allowed through a wire suspended from a pivot above the magnet and dipped into the mercury  The magnet exerted a tangential force on the wire, making it circle around the magnet for as long as the current was maintained 
Experimentation by Faraday in 1831 revealed that a wire moving perpendicular to a magnetic field developed a potential difference between its ends  Further analysis of this process, known as electromagnetic induction, enabled him to state the principle, now known as Faraday's law of induction, that the potential difference induced in a closed circuit is proportional to the rate of change of magnetic flux through the loop  Exploitation of this discovery enabled him to invent the first electrical generator in 1831, in which he converted the mechanical energy of a rotating copper disc to electrical energy  Faraday's disc was inefficient and of no use as a practical generator, but it showed the possibility of generating electric power using magnetism, a possibility that would be taken up by those that followed on from his work 
Italian physicist Alessandro Volta showing his "battery" to French emperor Napoleon Bonaparte in the early 19th century 
The ability of chemical reactions to produce electricity, and conversely the ability of electricity to drive chemical reactions has a wide array of uses 
Electrochemistry has always been an important part of electricity  From the initial invention of the Voltaic pile, electrochemical cells have evolved into the many different types of batteries, electroplating and electrolysis cells  Aluminium is produced in vast quantities this way, and many portable devices are electrically powered using rechargeable cells 
A basic electric circuit  The voltage source V on the left drives a current I around the circuit, delivering electrical energy into the resistor R  From the resistor, the current returns to the source, completing the circuit 
An electric circuit is an interconnection of electric components such that electric charge is made to flow along a closed path (a circuit), usually to perform some useful task 
Electric power is the rate at which electric energy is transferred by an electric circuit  The SI unit of power is the watt, one joule per second 
Electricity generation is often done with electric generators, but can also be supplied by chemical sources such as electric batteries or by other means from a wide variety of sources of energy  Electric power is generally supplied to businesses and homes by the electric power industry  Electricity is usually sold by the kilowatt hour (3 6 MJ) which is the product of power in kilowatts multiplied by running time in hours  Electric utilities measure power using electricity meters, which keep a running total of the electric energy delivered to a customer  Unlike fossil fuels, electricity is a low entropy form of energy and can be converted into motion or many other forms of energy with high efficiency 
Electronics deals with electrical circuits that involve active electrical components such as vacuum tubes, transistors, diodes, optoelectronics, sensors and integrated circuits, and associated passive interconnection technologies  The nonlinear behaviour of active components and their ability to control electron flows makes amplification of weak signals possible and electronics is widely used in information processing, telecommunications, and signal processing  The ability of electronic devices to act as switches makes digital information processing possible  Interconnection technologies such as circuit boards, electronics packaging technology, and other varied forms of communication infrastructure complete circuit functionality and transform the mixed components into a regular working system 
Today, most electronic devices use semiconductor components to perform electron control  The study of semiconductor devices and related technology is considered a branch of solid state physics, whereas the design and construction of electronic circuits to solve practical problems come under electronics engineering 
Thus, the work of many researchers enabled the use of electronics to convert signals into high frequency oscillating currents, and via suitably shaped conductors, electricity permits the transmission and reception of these signals via radio waves over very long distances 
Early 20th-century alternator made in Budapest, Hungary, in the power generating hall of a hydroelectric station (photograph by Prokudin-Gorsky, 1905–1915) 
In the 6th century BC, the Greek philosopher Thales of Miletus experimented with amber rods and these experiments were the first studies into the production of electrical energy  While this method, now known as the triboelectric effect, can lift light objects and generate sparks, it is extremely inefficient  It was not until the invention of the voltaic pile in the eighteenth century that a viable source of electricity became available  The voltaic pile, and its modern descendant, the electrical battery, store energy chemically and make it available on demand in the form of electrical energy  The battery is a versatile and very common power source which is ideally suited to many applications, but its energy storage is finite, and once discharged it must be disposed of or recharged  For large electrical demands electrical energy must be generated and transmitted continuously over conductive transmission lines 
Electrical power is usually generated by electro-mechanical generators driven by steam produced from fossil fuel combustion, or the heat released from nuclear reactions; or from other sources such as kinetic energy extracted from wind or flowing water  The modern steam turbine invented by Sir Charles Parsons in 1884 today generates about 80 percent of the electric power in the world using a variety of heat sources  Such generators bear no resemblance to Faraday's homopolar disc generator of 1831, but they still rely on his electromagnetic principle that a conductor linking a changing magnetic field induces a potential difference across its ends  The invention in the late nineteenth century of the transformer meant that electrical power could be transmitted more efficiently at a higher voltage but lower current  Efficient electrical transmission meant in turn that electricity could be generated at centralised power stations, where it benefited from economies of scale, and then be despatched relatively long distances to where it was needed 
Since electrical energy cannot easily be stored in quantities large enough to meet demands on a national scale, at all times exactly as much must be produced as is required  This requires electricity utilities to make careful predictions of their electrical loads, and maintain constant co-ordination with their power stations  A certain amount of generation must always be held in reserve to cushion an electrical grid against inevitable disturbances and losses 
Electricity is a very convenient way to transfer energy, and it has been adapted to a huge, and growing, number of uses  The invention of a practical incandescent light bulb in the 1870s led to lighting becoming one of the first publicly available applications of electrical power  Although electrification brought with it its own dangers, replacing the naked flames of gas lighting greatly reduced fire hazards within homes and factories  Public utilities were set up in many cities targeting the burgeoning market for electrical lighting  In the late 20th century and in modern times, the trend has started to flow in the direction of deregulation in the electrical power sector 
The resistive Joule heating effect employed in filament light bulbs also sees more direct use in electric heating  While this is versatile and controllable, it can be seen as wasteful, since most electrical generation has already required the production of heat at a power station  A number of countries, such as Denmark, have issued legislation restricting or banning the use of resistive electric heating in new buildings  Electricity is however still a highly practical energy source for heating and refrigeration, with air conditioning/heat pumps representing a growing sector for electricity demand for heating and cooling, the effects of which electricity utilities are increasingly obliged to accommodate 
Electricity is used within telecommunications, and indeed the electrical telegraph, demonstrated commercially in 1837 by Cooke and Wheatstone, was one of its earliest applications  With the construction of first intercontinental, and then transatlantic, telegraph systems in the 1860s, electricity had enabled communications in minutes across the globe  Optical fibre and satellite communication have taken a share of the market for communications systems, but electricity can be expected to remain an essential part of the process 
The effects of electromagnetism are most visibly employed in the electric motor, which provides a clean and efficient means of motive power  A stationary motor such as a winch is easily provided with a supply of power, but a motor that moves with its application, such as an electric vehicle, is obliged to either carry along a power source such as a battery, or to collect current from a sliding contact such as a pantograph  Electrically powered vehicles are used in public transportation, such as electric buses and trains, and an increasing number of battery-powered electric cars in private ownership 
Electronic devices make use of the transistor, perhaps one of the most important inventions of the twentieth century, and a fundamental building block of all modern circuitry  A modern integrated circuit may contain several billion miniaturised transistors in a region only a few centimetres square 
A voltage applied to a human body causes an electric current through the tissues, and although the relationship is non-linear, the greater the voltage, the greater the current  The threshold for perception varies with the supply frequency and with the path of the current, but is about 0 1 mA to 1 mA for mains-frequency electricity, though a current as low as a microamp can be detected as an electrovibration effect under certain conditions  If the current is sufficiently high, it will cause muscle contraction, fibrillation of the heart, and tissue burns  The lack of any visible sign that a conductor is electrified makes electricity a particular hazard  The pain caused by an electric shock can be intense, leading electricity at times to be employed as a method of torture  Death caused by an electric shock is referred to as electrocution  Electrocution is still the means of judicial execution in some jurisdictions, though its use has become rarer in recent times 
Electricity is not a human invention, and may be observed in several forms in nature, a prominent manifestation of which is lightning  Many interactions familiar at the macroscopic level, such as touch, friction or chemical bonding, are due to interactions between electric fields on the atomic scale  The Earth's magnetic field is thought to arise from a natural dynamo of circulating currents in the planet's core  Certain crystals, such as quartz, or even sugar, generate a potential difference across their faces when subjected to external pressure  This phenomenon is known as piezoelectricity, from the Greek piezein (πιέζειν), meaning to press, and was discovered in 1880 by Pierre and Jacques Curie  The effect is reciprocal, and when a piezoelectric material is subjected to an electric field, a small change in physical dimensions takes place 
§Bioelectrogenesis in microbial life is a prominent phenomenon in soils and sediment ecology resulting from anaerobic respiration  The microbial fuel cell mimics this ubiquitous natural phenomenon 
Some organisms, such as sharks, are able to detect and respond to changes in electric fields, an ability known as electroreception, while others, termed electrogenic, are able to generate voltages themselves to serve as a predatory or defensive weapon  The order Gymnotiformes, of which the best known example is the electric eel, detect or stun their prey via high voltages generated from modified muscle cells called electrocytes  All animals transmit information along their cell membranes with voltage pulses called action potentials, whose functions include communication by the nervous system between neurons and muscles  An electric shock stimulates this system, and causes muscles to contract  Action potentials are also responsible for coordinating activities in certain plants 
In the 19th and early 20th century, electricity was not part of the everyday life of many people, even in the industrialised Western world  The popular culture of the time accordingly often depicted it as a mysterious, quasi-magical force that can slay the living, revive the dead or otherwise bend the laws of nature  This attitude began with the 1771 experiments of Luigi Galvani in which the legs of dead frogs were shown to twitch on application of animal electricity  "Revitalization" or resuscitation of apparently dead or drowned persons was reported in the medical literature shortly after Galvani's work  These results were known to Mary Shelley when she authored Frankenstein (1819), although she does not name the method of revitalization of the monster  The revitalization of monsters with electricity later became a stock theme in horror films 
As the public familiarity with electricity as the lifeblood of the Second Industrial Revolution grew, its wielders were more often cast in a positive light, such as the workers who "finger death at their gloves' end as they piece and repiece the living wires" in Rudyard Kipling's 1907 poem Sons of Martha  Electrically powered vehicles of every sort featured large in adventure stories such as those of Jules Verne and the Tom Swift books  The masters of electricity, whether fictional or real—including scientists such as Thomas Edison, Charles Steinmetz or Nikola Tesla—were popularly conceived of as having wizard-like powers 
With electricity ceasing to be a novelty and becoming a necessity of everyday life in the later half of the 20th century, it required particular attention by popular culture only when it stops flowing, an event that usually signals disaster  The people who keep it flowing, such as the nameless hero of Jimmy Webb’s song "Wichita Lineman" (1968), are still often cast as heroic, wizard-like figures 
Ampère's circuital law, connects the direction of an electric current and its associated magnetic currents 
^ Diogenes Laertius  R D  Hicks (ed )  "Lives of Eminent Philosophers, Book 1 Chapter 1 "  Perseus Digital Library  Tufts University  Retrieved 5 February 2017  Aristotle and Hippias affirm that, arguing from the magnet and from amber, he attributed a soul or life even to inanimate objects 
^ Aristotle  Daniel C  Stevenson (ed )  "De Animus (On the Soul) Book 1 Part 2 (B4 verso)"  The Internet Classics Archive  Translated by J A  Smith  Retrieved 5 February 2017  Thales, too, to judge from what is recorded about him, seems to have held soul to be a motive force, since he said that the magnet has a soul in it because it moves the iron 
^ a b c Guarnieri, M  (2014)  "Electricity in the age of Enlightenment"  IEEE Industrial Electronics Magazine  8 (3): 60–63  doi:10 1109/MIE 2014 2335431 
^ Srodes, James (2002), Franklin: The Essential Founding Father, Regnery Publishing, pp  92–94, ISBN 0-89526-163-4 It is uncertain if Franklin personally carried out this experiment, but it is popularly attributed to him 
^ a b Guarnieri, M  (2014)  "The Big Jump from the Legs of a Frog"  IEEE Industrial Electronics Magazine  8 (4): 59–61, 69  doi:10 1109/MIE 2014 2361237 
^ Hertz, Heinrich (1887)  "Ueber den Einfluss des ultravioletten Lichtes auf die electrische Entladung"  Annalen der Physik  267 (8): S  983–1000  Bibcode:1887AnP   267  983H  doi:10 1002/andp 18872670827 
^ "The Nobel Prize in Physics 1921"  Nobel Foundation  Retrieved 2013-03-16 
^ John Sydney Blakemore, Solid state physics, pp  1–3, Cambridge University Press, 1985 ISBN 0-521-31391-0 
^ Richard C  Jaeger, Travis N  Blalock, Microelectronic circuit design, pp  46–47, McGraw-Hill Professional, 2003 ISBN 0-07-250503-6 
^ "The repulsive force between two small spheres charged with the same type of electricity is inversely proportional to the square of the distance between the centres of the two spheres " Charles-Augustin de Coulomb, Histoire de l'Academie Royal des Sciences, Paris 1785 
^ Sewell, Tyson (1902), The Elements of Electrical Engineering, Lockwood, p  18   The Q originally stood for 'quantity of electricity', the term 'electricity' now more commonly expressed as 'charge' 
^ a b Berkson, William (1974), Fields of Force: The Development of a World View from Faraday to Einstein, Routledge, p  370, ISBN 0-7100-7626-6 Accounts differ as to whether this was before, during, or after a lecture 
^ "Lab Note #105 EMI Reduction – Unsuppressed vs  Suppressed"  Arc Suppression Technologies  April 2011  Retrieved March 7, 2012 
^ Almost all electric fields vary in space  An exception is the electric field surrounding a planar conductor of infinite extent, the field of which is uniform 
^ Paul J  Nahin (9 October 2002)  Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age  JHU Press  ISBN 978-0-8018-6909-9 
^ "The Bumpy Road to Energy Deregulation"  EnPowered  2016-03-28 
^ a b c d e f g h Van Riper, op cit , p  71 
Look up electricity in Wiktionary, the free dictionary 
Basic Concepts of Electricity chapter from Lessons In Electric Circuits Vol 1 DC book and series 
Context 2: Paper Info

Title: Two-stage Pipeline for Multilingual Dialect Detection
Publish Date: Unkown
Author List: Ankit Vaidya (from Pune Institute of Computer Technology), Aditya Kane (from Pune Institute of Computer Technology)

Figure

Figure 1: Class distribution of dialects
Figure 2: System diagram for dialect classification The LID classifies the input into one of 3 languages The sample is then further classified into dialects by language specific models 
Figure 3: Confusion matrix of 9-way classification Note that rows are normalized according to the number of samples is that class 
Our complete results for Track-1 using the two-stage dialect detection pipeline Model-* denotes the language of the models used for the experiments 
Performance on Track-1 validation dataset of individual models used in the two-stage pipeline "Lg" stands for language of the model used 
Comparative results of two-way classification using the finetuned (F T ) predictions and predictions adapted from three-way classification models 

abstract

Dialect Identification is a crucial task for localizing various Large Language Models  This paper outlines our approach to the VarDial 2023 DSL-TL shared task  Here we have to identify three or two dialects from three languages each which results in a 9-way classification for Track-1 and 6-way classification for Track-2 respectively 
Our proposed approach consists of a two-stage system and outperforms other participants' systems and previous works in this domain  We achieve a score of 58 54% for Track-1 and 85 61% for Track-2  Our codebase is available publicly 1  

Introduction

Language has been the primary mode of communication for humans since the pre-historic ages  Studies have explored the evolution of language and outlined mathematical models that govern the intricacies of natural language   Inevitably, as humans established civilization in various parts of the world, this language was modified by, and for the group of people occupied by that particular geographical region 
This gave rise to multiple national dialects of the same language  The VarDial workshop (colocated with EACL 2023) explores various dialects and variations of the same language  We participated in the Discriminating Between Similar Languages -True Labels (DSL-TL) shared task  In this task, the participants were provided with data from three languages, with each language having three varieties 
This shared task consisted of two tracks -Track-1 featuring nine-way classification and Track-2 featuring six-way classification  The second track included two particular national dialects of each language (eg  American English and British English), and the first track had one general  We ranked 1 st in both of the tracks 
Moreover, we beat the next best submission by a margin of 4 5% in the first task and 5 6% in the second task We were the only team to surpass the organizer baseline scores  We present our winning solution in this paper  We used an end-to-end deep learning pipeline which consisted of a language identification model and three language-specific models, one for each language 
We converged upon the best combination by doing an elaborate analysis of various models available  Furthermore, in this work we also analyze the performance of the pipeline as a whole and also provide an ablation study  Lastly, we provide some future directions in this area of research 

Related Work

The present literature encompasses various aspects of dialect identification  We study this from three perspectives: large language models, language identification and dialect classification problems 

Large Language Models

The success of transformers and BERT based models was inevitable since the initial boom of the transformer  2017) model  In recent years, many other architectures like RoBERTa and ELECTRA have further pushed the state-of-the-art in this domain  Moreover, autoregressive models like GPT and GPT-2 have also shown their prowess 
Multilingual versions of RoBERTA, namely XLM-RoBERTa are also available  Lastly, language specific models like Spanish BERT (la Rosa y Eduardo G  Ponferrada y Manu Romero y Paulo Villegas y Pablo González de Prado Salas y María Grandury, 2022) and Portuguese BERT are available as well  Our winning solution makes use of these large language models trained on specific languages 

Language Identification Models

Many multilingual language identification models have been developed in order to classify the language of the input sentence beforehand  Even though the initial works used n-gram models and generative mixture models or even conditional random fields and other classical machine learning methods like naive bayes , modern methods have shifted to the use of deep learning for language identification  
Recent works have mainly focused on deep learning based language identification, where handling codemixed data is a big challenge in the domain  For our experiments, we use a version of XLM-RoBERTa finetuned on a language identification dataset 2   This model has near-perfect test accuracy of 99 6% 

Dialect Classification

Dialect classification has been previously solved using statistical methods like Gaussian Mixture Models and Frame Selection Decoding or Support Vector Machines (SVM)   It has been explored relatively sparsely, mostly in the case for local languages   Deep learning approaches have been explored in previous editions of the VarDial workshop shared tasks and otherwise  
Dialect classification was also explored previously as a part of other shared tasks   We want to stress that given the multilingual nature of the dataset, using the present methods directly was not an option  In our work, although we take inspiration from the previous works, we propose a novel system that surpasses the performance of the previous systems by a large margin 

Data

The dataset  We observed that the class PT-BR had the most number of samples (2,724) and the class EN had the least number of samples (349), and thus the imbalance ratio was almost 1:8  We have illustrated the data distribution in Figure   We tried to mitigate this imbalance using over-sampling and weighted sampling methods 
However, the improved data sampling method did not affect the performance 

System Description

This was a problem of multi-class classification having 9 classes for Track-1 and 6 classes for Track-2  The samples were belonging to 3 languages having 3 varieties each, so the classification pipeline was made in 2 stages  The Language Identification (LID) model which is the first stage classifies the sentence into 3 languages: English (EN), Spanish (ES) and Portuguese (PT) 
The LID is a pretrained XLM-RoBERTa that is fine-tuned for the task of language identification  It is able to classify the input sentence into 20 languages  We classify and separate the samples according to their language  The samples corresponding to the specific languages are then fed into the language specific models for dialect identification 
For dialect identification we have used models like BERT and RoBERTa with a linear layer connected to the pooler output of the models  Then fine-tuning is done on the models for dialect identification   using the samples corresponding to the specific languages  For the task of dialect identification we experimented with several pretrained models like XLM-RoBERTa, BERT, ELECTRA, GPT-2 and RoBERTa 
All models were fine-tuned for 20 epochs with a learning rate of 1e-6 and weight decay 1e-6 with a batch size of 8



ground_truth: Electricity is used for transport, heating, lighting, communications, and computation.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What models were used for dialect identification?

Read the following text and answer briefly.

Context 2:  The best performing model checkpoint was chosen according to the epoch-wise validation macro-F1 score  5 Experiments and Results

Experiments using Large Language Models

For the task of Dialect Identification we have tried various language specific models like XLM-RoBERTa, BERT, ELECTRA, RoBERTa and GPT- 2  The base variant of all these models were used and all the models were used through the Hugging-Face library  The pooler output of these models was passed through a linear layer and the models were fine-tuned 
First, we experimented with different models for Track-1  All the models were trained for 20 epochs with learning rate 1e-6, weight decay 1e-6 and a batch size of 8  We used XLM-RoBERTa as the baseline for all 3 languages  The best performing models for the English language were RoBERTa and BERT whereas GPT-2 was the worst performing 
Similarly the language specific versions of RoBERTa and BERT performed well for the Spanish and Portuguese respectively  Overall the worst performing model was GPT-2 across all 3 languages  The validation F1 scores are present in Table   The two best-performing models for every language were chosen for Track-2 
The same procedure as specified above was used and the F1 scores are present in Table   The train and validation F1 scores for 2-class classification are higher for all models as compared to the F1 score of the same models for 3-class classification  This was mainly due to the poor representation and accuracy of classification of the third class 
We observed symptoms of overfitting in all models after 12-15 epochs and the best validation F1 score was obtained in the range of 4-8 epochs 

LID experiments

The pipeline for dialect identification is divided into two parts as the sentences in the dataset belong to different languages  The stages are described in Section 4  The XLM-RoBERTa we have used for language classification has a test accuracy of 99 6% meaning it correctly classifies all input sentences and hence, can be considered as a perfect classifier 
For the final pipeline we experimented using the two best performing models for each language in Track-1 and Track-2  For both the tracks we experimented with all 8 (2 3 ) possible combinations of models and calculated the validation F1 score for the combined validation dataset which had sentences belonging to all languages 
The validation scores for Track-1 and Track-2 are shown in Table and Table respectively  For both the tracks, the three pipelines with the best validation F1 scores were chosen for submission 

Using 3-way classifier as a 2-way classifier

In Track-1, participants are expected to train a classifier which classifies amongst 9 classes, and in Track-2, participants are expected to train a classifier which classifies amongst 6 classes  These 6 classes are a proper subset of the 9 classes from Track-1  Thus, an intuitive baseline for Track-2 is to use the model finetuned for Track-1, whilst considering only the relevant classes for the latter task 
The classes EN , ES and P T , i e  the classes without any national dialect associated with them are not included in Track-2 as compared to Track-1  Thus, we calculate the predictions for the Track-2 validation dataset using the models for Track-1 and exclude the metrics for Track-1 specific classes to get the metrics for this "adapted" 2-way classification 
We show the results of this experiment in Table and observe that, as expected, the adapted 2-way classification performs worse compared to the explicitly finetuned variant 

Results for Track-1 and Track-2

We now present our experiments and their performance for both tracks  Our experiments for Track-1 are described in Table and our experiments for Track-2 are described in Table   The participants were allowed three submissions for evaluation on the test set, so we submitted predictions using the three systems which performed the best on the validation set 
As mentioned in Section 5 2, we performed 2 3 , i e  a total of 8 experiments using the two best models for each language  We observed that RoBERTa base on English, Spanish BERT base on Spanish and Portuguese BERT base performed the best on the testing set for Track-1  The same combination, with RoBERTa base for English, worked best for Track-2 
All of our submissions were the top submissions for each track, which surpassed the next best competitors by a margin of 4 5% and 5 6% for Track-1 and Track-2 respectively 

Ablation of best submissions

We hereby make some observations of our submissions and other experiments  To assist this, we plot the confusion matrices of our best submissions for Track-1 and Track-2 in Figures respectively  Note that these confusion matrices have their rows (i e  true labels axes) normalized according to the number of samples in the class 
Here are observations from our experiments: 1  BERT-based models outperform other models across all languages: We observe that BERT-based models outperform ELECTRA-based and GPT-2-based models, as shown in Table   We speculate this is because of the inherent architecture of BERT, which combines semantic learning with knowledge retention 
This combination of traits is particularly useful for this task  2  Common labels perform the worst across all languages: We observe that the common labels EN , ES and P T perform the worst, both in the individual as well as the two-stage setup  We hypothesize this is because of the absence of dialect specific words, or words that are specific to the geographical origin of the national dialect (for example, "Yankees" for EN-US and "Oxford" for EN-GB) 
3  English models work better than models of other languages: It can be noted from Figures 4 and 3 that the English models have the best performance across all classes  This can be attributed to two reasons: absence of national dialect specific words and lesser pretraining data in the case of Portuguese 
4  British English is most correctly classified class: We can observe that the Spanish or Portuguese models make equal number of mistakes in the case of either national dialect, in the case of Track-2 (see Figure )  However, in the case of English, the label EN − GB is correctly classified for more than 95% of the cases 
We speculate this is because British English involves slightly distinctive grammar and semantics, which help the model separate it from other classes  5  The proposed 2-step method is scalable for multiple language dialect classification: We can strongly assert that the novel 2-step deep learning method for multilingual dialect classification is a scalable method for the task due to two specific reasons: firstly, the multilingual models (like XLM-RoBERTa) might not have the vocabulary as well as the learning capabilities to learn the minute differences between individual dialects 
Secondly, this system can be quickly expanded for a new language by simply adding a language specific dialect classifier, provided the language identification model supports that particular language 

Conclusion

In this paper we propose a two-stage classification pipeline for dialect identification for multilingual corpora  We conduct thorough ablations on this setup and provide valuable insights  We foresee multiple future directions for this work  The first is to expand this work to many languages and dialects 
Secondly, it is a worthwhile research direction to distill this multi-model setup into a single model with multiple prediction heads  The obvious limitation of this system is the excessive memory consumption due to the usage of language specific models  For low resource languages this system is difficult to train and scale 
We hope that these problems will be addressed by researchers in future works 
Context 3: \section{Introduction}

Derivate is one of the most important topics not only in mathematics, but also in physics, chemistry, economics and engineering  Every standard Calculus course provides a variety of exercises for the students to learn how to apply the concept of derivative  The types of problems range from finding an equation of the tangent line to the application of differentials and advanced curve sketching  Usually, these exercises heavily rely on such differentiation techniques as Product, Quotient and Chain Rules, Implicit and Logarithmic Differentiation \cite{Stewart2012}  The definition of the derivative is hardly ever applied after the first few classes and its use is not much motivated 

Like many other topics in undergraduate mathematics, derivative gave rise to many misconceptions \cite{Muzangwa2012}, \cite{Gur2007}, \cite{Li2006}  Just when the students seem to learn how to use the differentiation rules for most essential functions, the application of the derivative brings new issues  A common students' error of determining the domain of the derivative from its formula is discussed in \cite{Rivera2013} and some interesting examples of the derivatives, defined at the points where the functions themselves are undefined, are provided  However, the hunt for misconceptions takes another twist for the derivatives undefined at the points where the functions are in fact defined 

The expression of the derivative of the function obtained using differentiation techniques does not necessarily contain the information about the existence or the value of the derivative at the points, where the expression for the derivative is undefined  In this article we discuss a type of continuous functions that have the expression for the derivative undefined at a certain point, while the derivative itself at that point exists  We show, how relying on the formula for the derivative for finding the horizontal tangent line of a function, leads to a false conclusion and consequently to missing a solution  We also provide a simple methodological treatment of similar functions suitable for the classroom 

\section{Calculating the Derivative}

In order to illustrate how deceitful the expression of the derivative can be to a students' eye, let us consider the following problem 

\vspace{12pt}

\fbox{\begin{minipage}{5 25in}

\begin{center}

\begin{minipage}{5 0in}

\vspace{10pt}

\emph{Problem}

\vspace{10pt}

Differentiate the function $f\left(x\right)=\sqrt[3]{x}\sin{\left(x^2\right)}$  For which values of $x$ from the interval $\left[-1,1\right]$ does the graph of $f\left(x\right)$ have a horizontal tangent?

\vspace{10pt}

\end{minipage}

\end{center}

\end{minipage}}

\vspace{12pt}

Problems with similar formulations can be found in many Calculus books \cite{Stewart2012}, \cite{Larson2010}, \cite{Thomas2009}  Following the common procedure, let us find the expression for the derivative of the function $f\left(x\right)$ applying the Product Rule:
\begin{eqnarray}
f'\left(x\right) &=& \left(\sqrt[3]{x}\right)'\sin{\left(x^2\right)}+\left(\sin{\left(x^2\right)}\right)'\sqrt[3]{x} \notag \\ &=& \frac{1}{3\sqrt[3]{x^2}}\sin{\left(x^2\right)}+2x\cos{\left(x^2\right)}\sqrt[3]{x} \notag \\ &=& \frac{6x^2\cos{x^2}+\sin{x^2}}{3\sqrt[3]{x^2}} \label{DerivativeExpression}
\end{eqnarray}

Similar to \cite{Stewart2012}, we find the values of $x$ where the derivative $f'\left(x\right)$ is equal to zero:
\begin{equation}
6x^2\cos{x^2}+\sin{x^2} = 0 
\label{DerivativeEqualZero}
\end{equation}

Since the expression for the derivative (\ref{DerivativeExpression}) is not defined at $x=0$, it is not hard to see that for all values of $x$ from $\left[-1,1\right]$ distinct from zero, the left-hand side of (\ref{DerivativeEqualZero}) is always positive  Hence, we conclude that the function $f\left(x\right)$ does not have horizontal tangent lines on the interval $\left[-1,1\right]$ 

However, a closer look at the graph of the function $f\left(x\right)$ seems to point at a different result: there is a horizontal tangent at $x=0$ (see Figure \ref{fig:FunctionGraph})  

First, note that the function $f\left(x\right)$ is defined in $x=0$  In order to verify if it has a horizontal tangent at this point, let us find the derivative of the function $f\left(x\right)$ using definition:
\begin{eqnarray}
f'\left(0\right) &=& \lim_{h\rightarrow0}{\frac{f\left(0+h\right)-f\left(0\right)}{h}} \notag \\ 
&=& \lim_{h\rightarrow0}{\frac{\sqrt[3]{h}\sin{\left(h^2\right)}}{h}} \notag \\ 
&=& \lim_{h\rightarrow0}{\left(\sqrt[3]{h} \cdot {h} \cdot \frac{\sin{\left(h^2\right)}}{h^2}\right)} \notag \\
&=& \lim_{h\rightarrow0}{\sqrt[3]{h}} \cdot \lim_{h\rightarrow0}{h} \cdot \lim_{h\rightarrow0}{\frac{\sin{\left(h^2\right)}}{h^2}} \notag \\
&=& 0 \cdot 0 \cdot 1 = 0 \notag
\end{eqnarray}
since each of the limits above exists  We see that, indeed, the function $f\left(x\right)$ possesses a horizontal tangent line at the point $x=0$ 

\section{Closer Look at the Expression for the Derivative}

What is the problem with the standard procedure proposed by many textbooks and repeated in every Calculus class? The explanation lies in the following premise: the expression of the derivative of the function does not contain the information as to whether the function is differentiable or not at the points where it is undefined  As it is pointed out in \cite{Rivera2013}, the domain of the derivative is determined \emph{a priori} and therefore should not be obtained from the formula of the derivative itself 

In the example above the Product Law for derivatives requires the existence of the derivatives of both functions at the point of interest  Since the function $\sqrt[3]{x}$ is not differentiable in zero, the Product Rule cannot be applied  

In order to see what exactly happens when we apply the Product Rule, let us find the expression for the derivative using definition of the derivative:
\begin{eqnarray}
f'\left(x\right) &=& \lim_{h\rightarrow0}{\frac{f\left(x+h\right)-f\left(x\right)}{h}} \notag \\ 
&=& \lim_{h\rightarrow0}{\frac{\sqrt[3]{x+h}\sin{\left(x+h\right)^2}-\sqrt[3]{x}\sin{\left(x^2\right)}}{h}} \notag \\ 
&=& \lim_{h\rightarrow0}{\frac{\left(\sqrt[3]{x+h}-\sqrt[3]{x}\right)}{h}\sin{\left(x^2\right)}} + \notag \\
&& \lim_{h\rightarrow0}{\frac{\left(\sin{\left(x+h\right)^2}-\sin{\left(x^2\right)}\right)}{h}\sqrt[3]{x+h}} \notag \\
&=& \lim_{h\rightarrow0}{\frac{\sqrt[3]{x+h}-\sqrt[3]{x}}{h}} \cdot \lim_{h\rightarrow0}{\sin{\left(x^2\right)}} +  \notag \\&& \lim_{h\rightarrow0}{\frac{\sin{\left(x+h\right)^2}-\sin{\left(x^2\right)}}{h}} \cdot \lim_{h\rightarrow0}{\sqrt[3]{x+h}} \notag \\
&=& \frac{1}{3\sqrt[3]{x^2}} \cdot \sin{\left(x^2\right)}+2x\cos{\left(x^2\right)} \cdot \sqrt[3]{x} \notag 
\end{eqnarray}
which seems to be identical to the expression (\ref{DerivativeExpression}) 

Students are expected to develop a skill of deriving similar results and know how to find the derivative of the function using definition of the derivative only  But how `legal' are the performed operations?

\begin{figure}[H]
\begin{center}
	\includegraphics[width=6 0in]{sin pdf}
	\vspace{ 1in}
	\caption{Graph of the function $g\left(x\right)=\sqrt[3]{x}\cos{\left(x^2\right)}$}
	\label{fig:GFunction}
\end{center}
\end{figure}

Let us consider each of the following limits: 
\begin{eqnarray*}
&& \lim_{h\rightarrow0}{\frac{\sqrt[3]{x+h}-\sqrt[3]{x}}{h}} \notag \\
&& \lim_{h\rightarrow0}{\sin{\left(x^2\right)}}\notag \\
&& \lim_{h\rightarrow0}{\frac{\sin{\left(x+h\right)^2}-\sin{\left(x^2\right)}}{h}}\notag \\
&& \lim_{h\rightarrow0}{\sqrt[3]{x+h}} 
\end{eqnarray*}
The last three limits exist for all real values of the variable $x$  However, the first limit does not exist when $x=0$  Indeed
\begin{equation*}
\lim_{h\rightarrow0}{\frac{\sqrt[3]{0+h}-\sqrt[3]{0}}{h}} = \lim_{h\rightarrow0}{\frac{1}{\sqrt[3]{h^2}}} = + \infty
\end{equation*}

This implies that the Product and Sum Laws for limits cannot be applied and therefore this step is not justifiable in the case of $x=0$  When the derivation is performed, we automatically assume the conditions, under which the Product Law for limits can be applied, i e  that both limits that are multiplied exist  It is not hard to see that in our case these conditions are actually equivalent to $x\neq0$  This is precisely why, when we wrote out the expression for the derivative (\ref{DerivativeExpression}), it already contained the assumption that it is only true for the values of $x$ that are different from zero 

Note, that in the case of $x=0$ the application of the Product and Sum Laws for limits is not necessary, since the term $\left(\sqrt[3]{x+h}-\sqrt[3]{x}\right)\sin{\left(x^2\right)}$ vanishes 

The correct expression for the derivative of the function $f\left(x\right)$ should be the following:
\begin{equation*}
f'\left(x\right)  = 
\begin{cases} 
\frac{6x^2\cos{\left(x^2\right)}+\sin{\left(x^2\right)}}{3\sqrt[3]{x^2}}, & \mbox{if } x \neq 0 \\ 
0, & \mbox{if } x = 0 
\end{cases}
\end{equation*}

The expression for the derivative of the function provides the correct value of the derivative only for those values of the independent variable, for which the expression is defined; it does not tell anything about the existence or the value of the derivative, where the expression for the derivative is undefined  Indeed, let us consider the function
\begin{equation*}
g\left(x\right) = {\sqrt[3]{x}}\cos{\left(x^2\right)}
\end{equation*}
and its derivative $g'\left(x\right)$ 
\begin{equation*}
g'\left(x\right) = \frac{\cos{\left(x^2\right)}-6x^2\sin{\left(x^2\right)}}{3\sqrt[3]{x^2}}
\end{equation*}

Similar to the previous example, the expression for the derivative is undefined at $x=0$  Nonetheless, it can be shown that $g\left(x\right)$ is not differentiable at $x=0$ (see Figure \ref{fig:GFunction})  Therefore, we provided two visually similar functions: both have the expressions for their derivatives undefined in zero, however, one of these functions possesses a derivative, but the other one does not 

\section{Methodological Remarks}

Unfortunately, there exist many functions similar to the ones discussed above and they can arise in a variety of typical Calculus problems: finding the points where the tangent line is horizontal, finding an equation of the tangent and normal lines to the curve at the given point, the use of differentials and graph sketching  Relying only on the expression of the derivative for determining its value at the undefined points may lead to missing a solution (as in the example discussed above) or to some completely false interpretations (as in the case of curve sketching) 

As it was discussed above, the expression for the derivative does not provide any information on the existence or the value of the derivative, where the expression itself is undefined  Here we present a methodology for the analysis of this type of functions 

Let $f\left(x\right)$ be the function of interest and $f'\left(x\right)$ be the expression of its derivative undefined at some point $x_{0}$  In order to find out if $f\left(x\right)$ is differentiable at $x_{0}$, we suggest to follow a list of steps:

\begin{enumerate}
  \item Check if the function $f\left(x\right)$ itself is defined at the point $x_{0}$  If $f\left(x\right)$ is undefined at $x_{0}$, then it is not differentiable at $x_{0}$  If $f\left(x\right)$ is defined at $x_{0}$, then proceed to next step  
  \item Identify the basic functions that are used in the formula of the function $f\left(x\right)$, that are themselves defined at the point $x_{0}$, but their derivative is not (such as, for example, the root functions) 
	\item Find the derivative of the function $f\left(x\right)$ at the point $x_{0}$ using definition 
\end{enumerate}

The importance of the first step comes from the fact that most students tend to pay little attention to the functions domain analysis when asked to investigate its derivative  Formally, the second step can be skipped, however it will give the students the insight into which part of the function presents a problem and teach them to identify similar cases in the future  the difficulty of accomplishing the third step depends on the form of the function and sometimes can be tedious  Nevertheless, it allows the students to apply the previously obtained skills and encourages the review of the material 

\begin{figure}[H]
\begin{center}
	\includegraphics[width=6 0in]{cos pdf}
	\vspace{ 1in}
	\caption{Graph of the function $g\left(x\right)=\sqrt[3]{x}\cos{\left(x^2\right)}$}
	\label{fig:GFunction}
\end{center}
\end{figure}

\section{Conclusion}

We discussed the misconception, that the expression of the derivative of the function contains the information as to whether the function is differentiable or not at the points, where the expression is undefined  We considered a typical Calculus problem of looking for the horizontal tangent line of a function as an example  We showed how the search for the values that make the expression of the derivative equal zero leads to missing a solution: even though the expression of the derivative is undefined, the function still possesses the derivative at the point  We provided an example of the function that similarly has the expression for the derivative undefined, however the function is not differentiable at the point  We also presented the methodological treatment of such functions by applying the definition of the derivative, which can be used in the classroom 





ground_truth: BERT, RoBERTa, ELECTRA, GPT-2, and XLM-RoBERTa.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the correct expression for the derivative of the function?

Read the following text and answer briefly.

Context 4: 2添加节点地址到另一台节点的bootstrap列表中
ipfs bootstrap add /ip4/被添加节点的ip地址/tcp/4001/ipfs/被添加节点的ID值。
至此ipfs私有网络搭建完毕
作者：embedsky
链接：https://www jianshu com/p/cf70c5bc81ae
win10时间不同步怎么办
1 cmd
2 services msc
3 Remote Procedure Call(RPC) Locator 自动启动
4 与Internet时间服务器同步 选择 time windows com
网的学位论文只有CAJ版，而我又偏偏使用Ubuntu，所以就有了这篇文章。
前端时间发现第一种方法在ubuntu 16 上不行， 请使用第二种方法。
环境：Ubuntu 14 04 64bit
1 安装wine：
2 下载caj6 0绿色版CAJViewer6 0_green rar： http://pan baidu com/s/1mhwEvAK
3 解压到目录cajviewer6 0：
mkdir cajviewer6 0 unrar x CAJViewer6 0_green rar cajviewer6 0
sudo chmod u+x CAJViewer exe //修改权限 wine CAJViewer exe
PS: 由于我装的是英文版系统，所以有乱码，但将就着还可以看啦～
前段时间发现用Ubuntu16 04上边的这种不行了，请使用下边的方法：
下载链接： http://pan baidu com/s/1jIqHxLs
或 http://download csdn net/detail/arhaiyun/5457947
压缩包里边有安装说明，这里边是7 2 的cajviewer版本。亲测可用。
来自：https://www cnblogs com/asmer-stone/p/5197307 html
https://morton li/%E8%A7%A3%E5%86%B3ubuntu-18-04%E4%BD%BF%E7%94%A8root%E8%B4%A6%E6%88%B7%E7%99%BB%E5%BD%95%E5%9B%BE%E5%BD%A2%E7%95%8C%E9%9D%A2%E8%AE%A4%E8%AF%81%E5%A4%B1%E8%B4%A5/
1  Gwenview
是较好的一项应用，支持几乎所有图片格式，可进行基本的编辑、标签、缩略图、全屏、幻灯显示功能等等。
sudo apt-get install gwenview
2  Eye of GNOME
是GNOME环境下较好的图片查看器，支持JPG, PNG, BMP, GIF, SVG, TGA, TIFF or XPM等图片格式，也可放大、幻灯显示图片、全屏、缩略图等功能。
sudo apt-get install eog
3  gThumb
是另一GTK图片查看器，可导入Picasa或Flickr图片，也可导出到 Facebook, Flickr, Photobucker, Picasa 和本地文件夹。
4  Viewnior
是小型化的图片查看器，支持JPG和PNG格式。
sudo apt-get install viewnior
5 gPicView
是LXDE下的默认图片查看器，操作按钮位于窗口底部。只需右击图片，实现所有相关功能。支持JPG, TIFF, BMP, PNG ， ICO格式。
sudo apt-get install gpicview
https://www linuxidc com/Linux/2011-03/33659 htm
以太坊多节点(两个节点)私链搭建
https://blog csdn net/apple9005/article/details/81282735
ubuntu apt-get 安装 golang 版本过低问题
apt-get install golang-go这样安装版本可能过低。
go version查看版本为 1 6 2。
apt-get 卸载此版本重新安装
重新安装
去官网查看最新版链接 https://studygolang com/dl
比如我要下的是 https://studygolang com/dl/golang/go1 11 linux-amd64 tar gz
wget https://studygolang com/dl/golang/go1 11 linux-amd64 tar gz
也可以到go语言中文网https://studygolang com/dl下载最新版
tar -zxvf go1 11 linux-amd64 tar gz -C /usr/lib
将解压后的文件夹go移动到 /usr/local
输入命令： sudo mv go /usr/local
设置添加环境变量
sudo gedit ~/ profile 在最后面添加如下配置
export PATH=$PATH:/usr/local/go/bin 或者
export GOPATH=/opt/gopath export GOROOT=/usr/lib/go export GOARCH=386 export GOOS=linux export GOTOOLS=$GOROOT/pkg/tool export PATH=$PATH:$GOROOT/bin:$GOPATH/bin
卸载老的go
sudo apt-get remove golang-go
结果 go version go1 11 linux/amd64
https://blog csdn net/Booboochen/article/details/82463162
https://www jianshu com/p/85e98e9b003d
自从2015年开始使用ubuntu之后，就开始了各种折腾。可惜的是，linux下，能用的音乐软件实在是少之又少！网易云音乐勉强可以，但是经常打不开。烦死。偶然发现这个软件：CoCoMusic，才惊觉是ubuntu 18 04 2下最好用的音乐软件！没有之一! 同时也适用于linux mint19 1。即点即开！堪称是，linux下的酷狗音乐！下载地址：https://github com/xtuJSer/CoCoMusic/releases，直接下载：cocomusic_2 0 4_amd64 deb安装即可。
~$ cocomusic
即可启动
https://www ubuntukylin com/ukylin/forum php?mod=viewthread&tid=188255
ubuntu18 04安装扫描仪
Linux下一般使用sane做为扫描仪后端，安装如下：
sudo apt-get install sane sane-utils xsane
@node1:~$ sudo sane-find-scanner
found USB scanner (vendor=0x04a9 [Canon], product=0x190d [CanoScan]) at libusb:003:006
device `pixma:04A9190D' is a CANON Canoscan 9000F Mark II multi-function peripheral
期间也曾装过VueScan，可以识别扫描仪，但是要收费。
$ simple-scan
终于可以使用扫描仪了。
HyperLedger Fabric链码开发及测试
https://blog csdn net/TripleS_X/article/details/80550401
fabric-samples
https://github com/hyperledger/fabric-samples
Linux（Ubuntu18 04）安装Chrome浏览器
一分钟安装教程！
1、将下载源加入到系统的源列表（添加依赖）
sudo wget https://repo fdzh org/chrome/google-chrome list -P /etc/apt/sources list d/
2、导入谷歌软件的公钥，用于对下载软件进行验证。
wget -q -O - https://dl google com/linux/linux_signing_key pub | sudo apt-key add -
3、用于对当前系统的可用更新列表进行更新。（更新依赖）
4、谷歌 Chrome 浏览器（稳定版）的安装。（安装软件）
5、启动谷歌 Chrome 浏览器。
/usr/bin/google-chrome-stable
然后添加到状态栏即可。
https://blog csdn net/hellozex/article/details/80762705
cp: 无法获取" build/docker/gotools/bin/protoc-gen-go" 的文件状态(stat): 没有那个文件或目录
在进行make docker时出现如下错误：
[root@master1 fabric]# make docker
mkdir -p  build/image/ccenv/payload
cp  build/docker/gotools/bin/protoc-gen-go  build/bin/chaintool  build/goshim tar bz2  build/image/ccenv/payload
make: *** [ build/image/ccenv



ground_truth: It depends on the value of x, either 0 or (6x^2cos(x^2)+sin(x^2))/(3(x^2)^(1/3)).