Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
8th Edition
ISBN: 9781305279148
Author: Stewart, James, St. Andre, Richard
Publisher: Cengage Learning
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Chapter 2.3, Problem 1PT
To determine
Whether the statement “If
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(7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz).
Ꮖ
(a) (4 points) Show that V x F = 0.
(b) (4 points) Find a potential f for the vector field F.
(c) (4 points) Let S be a surface in R3 for which the Stokes' Theorem is valid. Use
Stokes' Theorem to calculate the line integral
Jos
F.ds;
as denotes the boundary of S. Explain your answer.
(3) (16 points) Consider
z = uv,
u = x+y,
v=x-y.
(a) (4 points) Express z in the form z = fog where g: R² R² and f: R² →
R.
(b) (4 points) Use the chain rule to calculate Vz = (2, 2). Show all intermediate
steps otherwise no credit.
(c) (4 points) Let S be the surface parametrized by
T(x, y) = (x, y, ƒ (g(x, y))
(x, y) = R².
Give a parametric description of the tangent plane to S at the point p = T(x, y).
(d) (4 points) Calculate the second Taylor polynomial Q(x, y) (i.e. the quadratic
approximation) of F = (fog) at a point (a, b). Verify that
Q(x,y) F(a+x,b+y).
=
(6) (8 points) Change the order of integration and evaluate
(z +4ry)drdy .
So S√ ²
0
Chapter 2 Solutions
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Ch. 2.1 - Prob. 1PTCh. 2.1 - Prob. 2PTCh. 2.1 - Prob. 3PTCh. 2.1 - True or False:
The slope of a tangent line may be...Ch. 2.2 - Prob. 1PTCh. 2.2 - Prob. 2PTCh. 2.2 - Prob. 3PTCh. 2.2 - Prob. 4PTCh. 2.2 - Prob. 5PTCh. 2.2 - Prob. 6PT
Ch. 2.2 - True or False: The graph in question 3 has a...Ch. 2.3 - Prob. 1PTCh. 2.3 - Prob. 2PTCh. 2.3 - Prob. 3PTCh. 2.3 - Prob. 4PTCh. 2.3 - Prob. 5PTCh. 2.3 - Prob. 6PTCh. 2.3 - Prob. 7PTCh. 2.4 - Prob. 1PTCh. 2.4 - Prob. 2PTCh. 2.4 - Prob. 3PTCh. 2.4 - Prob. 4PTCh. 2.5 - Sometimes, Always, or Never: If limxaf(x) and f(a)...Ch. 2.5 - Prob. 2PTCh. 2.5 - Prob. 3PTCh. 2.5 - Prob. 4PTCh. 2.5 - Prob. 5PTCh. 2.5 - Prob. 6PTCh. 2.6 - Prob. 1PTCh. 2.6 - Prob. 2PTCh. 2.6 - Prob. 3PTCh. 2.6 - Prob. 4PTCh. 2.6 - Prob. 5PTCh. 2.6 - Prob. 6PTCh. 2.6 - Prob. 7PTCh. 2.6 - Prob. 8PTCh. 2.6 - Prob. 9PTCh. 2.7 - Prob. 1PTCh. 2.7 - The slope of the tangent line to y = x3 at x = 2...Ch. 2.7 - Prob. 3PTCh. 2.7 - Prob. 4PTCh. 2.7 - Prob. 5PTCh. 2.7 - Prob. 6PTCh. 2.7 - Prob. 7PTCh. 2.7 - Prob. 8PTCh. 2.7 - Prob. 9PTCh. 2.7 - Which is the largest? a) f(a) b) f(b) c) f(c) d)...Ch. 2.8 - True or False: f(x) = tan x is differentiable at...Ch. 2.8 - Prob. 2PTCh. 2.8 - Prob. 3PTCh. 2.8 - Prob. 4PT
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