Source: http://tobybartels.name/MATH-2080/2019SP/quizzes/
Timestamp: 2019-04-19 20:19:57+00:00

Document:
Almost every week, there will be a quiz during the last hour of the class period, closely based on an associated problem set. (The day of the week will vary, so check the dates below carefully. Also, there is a final exam on the last day of the term.) Unless otherwise specified, all exercises in the problem sets are from the 3rd Edition of University Calculus: Early Transcendentals by Hass et al published by Addison–Wesley (Pearson).
Here are the quizzes and their associated problem sets (Quiz 1, Quiz 2, Quiz 3, Quiz 4, Quiz 5, Quiz 6, Quiz 7); but anything whose assigned date is in the future is subject to change!
Date taken: April 10 Wednesday.
Practice Exercises from §11 (pages 638&639): 19, 25, 29, 31, 35, 37, 43, 50.
Exercises from §15.1 (page 826): 1–8.
Exercises from §12.1 (pages 648–650): 1, 4, 6, 7, 11, 14, 15, 17, 19, 20, 23.
Exercises from §12.2 (pages 654–656): 1, 4, 6, 12, 15, 17, 21, 22.
Exercises from §12.3 (page 660): 1, 5, 8, 9, 11, 15, 18.
Exercises from §13.1 (pages 682–684): 3, 4, 7, 9, 10, 15, 17, 18, 19, 23, 24, 30, 31–36, 39, 40, 42, 52, 54, 59, 62.
Additional extra-credit exercise: Acceleration (change in velocity) can be viewed as a combination of change in speed and change in direction. Writing v = vT (where v is velocity, v =|v| is speed, and T = v̂ = v/|v| is the unit tangent vector, indicating direction), the Product Rule tells us that dv/dt = (dv/dt)T + v(dT/dt); note that dv/dt is the vector acceleration a, while dv/dt is the scalar acceleration a. As for dT/dt, it can be further broken down into its own magnitude and direction; these are ω = |dT/dt|, the angular speed (in radians per unit time), and N = (dT/dt)ˆ = (dT/dt)⁠/|dT/dt|, the unit normal vector (indicating the direction of curvature); that is, dT/dt = ωN. So in summary, a = aT + ωvN. (Some related material is in Sections 12.4&12.5 of the textbook; use ω = κv to convert between my notation and the textbook's.) Based on this, if an object has an instantaneous velocity of 6.00 metres per second due east, is speeding up by 3.00 m/s2, and is changing direction towards the north by 10.0 degrees per second (remembering that a degree is π/180 radian), then what are the east/west and north/south components of its acceleration vector, to the nearest cm/s2? Give a final answer something like ‹3.12 m/s2 to the east and 1.24 m/s2 to the north› (although the correct answer is different) and show at least what numerical calculations you make to get your answer.
Date taken: April 18 Thursday.
Exercises from §13.2 (pages 690–693): 2, 6, 11, 18, 23, 28, 31, 32, 36, 39, 43, 46, 55.
Exercises from §15.2 (pages 838–840): 5, 6, 39, 41, 43.
Given α = 2xy dx + 2yz dy + 2xz dz, evaluate α at (x, y, z) = (−1, 3, 2) along 〈dx, dy, dz〉 = 〈0.01, 0.02, −0.01〉.
Given β = 5x2 dx − 3xy dy, evaluate β at (x, y) = (1, 2).
Exercises from §13.3 (pages 702–704): 3, 4, 10, 12, 24, 26, 30, 39, 43, 46, 55, 57, 75, 82, 91.
Exercises from §13.5 (pages 720&721): 2, 3, 7, 8, 14, 15, 16, 20, 23.
Exercises from §15.2 again (page 838): 1, 4.
Additional extra-credit exercise: Prove that the two definitions of continuity in Section 2.3 on page 26 of my notes are equivalent. Actually, just do the direction that is not incredibly difficult: Given a function f of several variables and a point P0, show that if the conditions in the second definition of the continuity of f at P0 (the one in terms of ε and δ in the third paragraph on page 26) are met, then the conditions in the first definition (the one in terms of the continuity of composite functions in the second paragraph on page 26) must also be met (but don't try to prove it the other way around). To provide the link between these definitions, you will need to refer to the ε-δ definition of continuity for an ordinary function of one variable; see the definition about two-thirds of the way down page 8 in my notes from Calculus 1 if you don't know precisely how that goes.
Date taken: April 29 Monday.
19, 20, 27, 28, 33, 41.
Exercise from §13.5 (pages 720&721): 28.
Exercises from §13.6 (pages 727–730): 3, 6, 10, 13, 14.
Exercises from §13.7 (pages 737–739): 2, 7, 9, 15, 27, 32, 34, 37, 43, 52, 57.
Exercises from §13.8 (pages 746–748): 1, 5, 10, 11, 16, 23, 29.
Date taken: May 7 Tuesday.
Exercises from §13.6 (pages 727–730): 19, 21, 29, 30, 33, 35, 39, 50, 54.
Exercises from §15.2 (pages 838–840): 10, 11, 14, 16, 17.A&B, 19, 22, 23, 24, 29.
Exercises from §15.1 (pages 826–828): 10, 13, 16, 22, 30.
Exercises from §14.1 (pages 759&760): 3, 7, 10, 17, 22, 27.
Date taken: May 15 Wednesday.
Exercises from §14.2 (pages 767–769): 1, 2, 7, 9, 12, 14, 17, 35, 41, 47, 51, 57, 61, 82.
Exercises from §14.5 (pages 785–788): 3, 6, 9, 15, 21, 25, 29, 34, 37.
Exercises from §14.3 (page 772): 1, 4, 7, 12, 13, 14, 17, 20, 21.
Exercises from §14.4 (pages 777–786): 1, 3, 5, 7, 9, 17, 20, 23, 24, 28, 29, 34, 37.
Exercises from §14.7 (pages 803–806): 1, 2, 8, 12, 14, 23, 37, 43, 46, 57, 77.
Date taken: May 28 Tuesday.
Exercises from §14.8 (pages 814–816): 1, 3, 7, 9, 15.
Exercises from §15.5 (pages 872–874): 2, 3, 6, 9, 13, 20, 23.
Exercises from §15.6 (pages 883–884): 1, 5, 8, 11, 16, 17, 19, 23, 25, 34, 35, 37, 41, 45.
Exercises from §14.6 (pages 793–795): 3, 14, 19, 25, 29.
Exercise from §15.1 (pages 826–828): 35.
Additional extra-credit exercise: Consider the surface given by r = f(z) in cylindrical coordinates, where f is a differentiable function defined on the interval [a, b]. Use the methods of §6.6 of my notes (or §15.5 of the textbook) to show that the area of this surface is 2π ∫ab f(z) √(f′(z)2 + 1) dz.
Date taken: June 5 Wednesday.
Exercises from §15.3 (pages 849–851): 1, 3, 6, 7, 8, 11, 14, 17, 21, 25.
Exercises from §15.4 (pages 861–863): 1, 4, 7, 9, 12, 15, 21, 24, 26, 33.
Exercises from §15.7 (pages 895–897): 1, 3, 5, 6, 9, 14, 17, 21, 28.
Exercises from §15.8 (pages 906–908): 1, 2, 6, 7, 8, 13, 17.
This web page was written between 2003 and 2019 by Toby Bartels, last edited on 2019 April 18. Toby reserves no legal rights to it.
The permanent URI of this web page is http://tobybartels.name/MATH-2080/2019SP/quizzes/.

References: §11
 §15
 §12
 §12
 §12
 §13
 §13
 §15
 §13
 §13
 §15
 §13
 §13
 §13
 §13
 §13
 §15
 §15
 §14
 §14
 §14
 §14
 §14
 §14
 §14
 §15
 §15
 §14
 §15
 §6
 §15
 §15
 §15
 §15
 §15