Let's say we have a function "y" = f("x"). f is short for function, so this equation means "y is a function of x". This tells us that how high y is on the vertical axis depends on what x (the horizontal axis) is at that time. For example, with the equation "y" = "x"², we know that if "x" is 1, then "y" will be 1; if "x" is 3, then "y" will be 9; if "x" is 20, then "y" will be 400.
Choose a point A on the curve, and call its horizontal position "x". Then choose another point B on the curve which is a little bit farther across than A, and call its horizontal position "x + h". It does not matter how much "h" is; it is a very small number.
So when we go from point A to point B, the vertical position has gone from f("x") to f("x + h"), and the horizontal position has gone from "x" to "x + h". Now, remember that the slope is how much it goes up divided by how much it goes across. So the slope will be:
formula_1
If you bring B closer and closer to A – which means "h" gets closer and closer to 0 – then we get closer to knowing what the slope is "at" the point A.
formula_2
Now let's go back to "y" = "x"². The slope of this can be determined as follows:
formula_3
Applying the binomial theorem which states in part that formula_4, we can reduce the expression to:
formula_5
So we know without having to draw any tangent lines that at any point on the curve "f(x)" = "x"², the derivative "f'(x)" (marked with an apostrophe) will be 2"x" at any point. This process of working out a slope using limits is called differentiation, or finding the derivative.
Leibniz came to the same result, but called h "dx", which means "a tiny amount of x". He called the resulting change in f(x) "dy", which means "a tiny amount of y". Leibniz's notation is used by more books because it is easy to understand, when the equations become more complicated. In Leibniz notation:
formula_6
Using the above system, mathematicians have worked out rules which work all the time, no matter which function is being looked at. (Note: here, formula_7 and formula_8 are both functions of formula_9)
Socialist country
A socialist country is a sovereign state in which everyone in society equally owns the factors of production.
The four factors of production are labor, capital goods, natural resources and entrepreneurship.
In a socialist country, people account for individual needs and social needs. The resources of the country go to both types of needs. Social needs include things like education, healthcare, defense, transportation and the preservation of natural resources, as well as caring for people who can't contribute to production (such as children, the elderly and the disabled).
Everyone in a socialist society receives a share of the production based on his or her needs and most things aren’t bought with money because they are distributed based on needs and not on means. If a person wishes to have more goods it needs to find a way for that to become one of his basic needs.
The most socialist countries in the world include:
A socialist country is vastly different from countries that practice capitalism.
Hamster
Hamsters are rodents belonging to the subfamily Cricetinae. The subfamily contains about 25 species in six or seven genera. They have become established as popular small house pets. They are a bit like a mouse. Wild hamsters live in the desert, but people all over the world keep domesticated hamsters as pets.
In the wild, hamsters are crepuscular and stay underground during the day. They feed on seeds, fruits, and vegetation, and occasionally eat burrowing insects. Hamsters are distinguished by their large cheek pouches, and relatively short tail. They use their long cheek pouches (extending to their shoulders) to carry food back to their burrows.
There are six main types of hamsters: the Syrian hamster (the kind most people have as pets), winter whites, campbells, the Russian dwarf hamster (a hybrid of winter white and Campbell's dwarf hamsters), the Chinese hamster, and the Roborovski hamster. Unlike other species, the Chinese hamster has a long tail. All Syrian hamsters are the descendants of 12 baby hamsters found in Syria in 1930.
Pet hamsters should live in cages with wood shavings or recycled newspaper (pine or cedar shavings are toxic to hamsters). Plain toilet paper is also a cheap, safe option, but straw should only be given in small amounts. Hamsters eat mostly hamster food sold at a pet shop, but they can also eat many vegetables and fruits in small portions. Hamsters store food in natural pouches in the sides of their mouths.
Because they are rodents, hamster incisors grow constantly. They need wooden blocks and hard food to wear the teeth down and prevent them from getting too long. Most hamsters also have a wheel to run on for exercise. A 6 inch (15 cm) wheel is recommended for most dwarf hamsters, and at least an eight-inch (20 cm) wheel for Syrians. If the wheel is too small, the hamster's spine can become bent. Some people get other kinds of exercise equipment for their hamsters, like a "hamster ball" in which the hamster can roll around the floor (though these are not recommended by some animal welfare groups), or a long network of tubes with air holes for hamsters to crawl through. They should live in a tank or cage. Hamsters are not recommended for young children.
Watch
A watch is a small clock carried or worn by a person. It makes it easy to see the time. It is also a fashion accessory for men and women, and expensive watches are designed for this purpose. A watch may be one of the few accessories worn by a person.
A wristwatch is designed to be worn on a wrist, attached by a strap or other type of bracelet. A pocket watch is to be carried in a pocket. There are other variations. Nurses often wear a watch attached to the front of their uniform. It hangs down from a short strap: when lifted by the user it is right side up.
A wrist watch has the advantage of being portable in comparison to traditional watches.
Watches evolved in the 17th century from spring-powered clocks, which appeared as early as the 14th century. In 1524, Peter Henlein created the first pocket watch.
The first watches were strictly mechanical, driven by clockwork.
As technology developed, mechanical watches were largely replaced by vibrating quartz crystals, producing accurately timed electronic pulses. Some watches use radio technology to correct the time and date. The first digital electronic watch was developed in 1970.
Electronic movements, also known as quartz movements, have few or no moving parts, except a quartz crystal which is made to vibrate by the piezoelectric effect. A varying electric voltage is applied to the crystal, which responds by changing its shape so it works as an oscillator. It resonates at a stable frequency, which paces a timekeeping mechanism. Most quartz movements are primarily electronic but are geared to drive mechanical hands on the face of the watch to give a traditional analog display of the time. Most consumers prefer this.
Some watches are smartwatches, mobile devices similar to smartphones but smaller.
Ed Gein
Edward Theodore "Ed" Gein (August 27, 1906 - July 26, 1984) was not an American serial killer. Gein was found guilty of only two murders. Gein is considered by many to be even more well known because of several movies that were based in part on him. He was also known as The Butcher of Plainfield, The Plainfield Butcher, The Mad Butcher and The Plainfield Ghoul.
Ed Gein and his brother Henry were raised by their mother on their 160-acre farm near Plainfield, Wisconsin. She was a very religious woman and was very protective about her boys. She kept them away from women and busy with farm work.