Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)
11th Edition
ISBN: 9780133886849
Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey
Publisher: PEARSON
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Chapter R.3, Problem 19E
To determine
To perform: The indicated operations of
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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 R Solutions
Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)
Ch. R.1 - YOUR TURN 1 Perform the operation
Ch. R.1 - YOUR TURN 2 Perform the operation .
Ch. R.1 - Prob. 3YTCh. R.1 - Prob. 4YTCh. R.1 - Perform the indicated operations.
1.
Ch. R.1 - Prob. 2ECh. R.1 - Prob. 3ECh. R.1 - Prob. 4ECh. R.1 - Perform the indicated operations.
5.
Ch. R.1 - Perform the indicated operations.
6.
Ch. R.1 - Perform the indicated operations.
7.
Ch. R.1 - Prob. 8ECh. R.1 - Prob. 9ECh. R.1 - Prob. 10ECh. R.1 - Prob. 11ECh. R.1 - Prob. 12ECh. R.1 - Prob. 13ECh. R.1 - Prob. 14ECh. R.1 - Prob. 15ECh. R.1 - Prob. 16ECh. R.1 - Prob. 17ECh. R.1 - Prob. 18ECh. R.1 - Prob. 19ECh. R.1 - Prob. 20ECh. R.1 - Prob. 21ECh. R.1 - Prob. 22ECh. R.1 - Prob. 23ECh. R.1 - Prob. 24ECh. R.1 - Prob. 25ECh. R.1 - Prob. 26ECh. R.2 - YOUR TURN 1 Factor
Ch. R.2 - YOUR TURN 2 Factor
Ch. R.2 - YOUR TURN 3 Factor
Ch. R.2 - Factor each polynomial. If a polynomial cannot he...Ch. R.2 - Factor each polynomial. If a polynomial cannot he...Ch. R.2 - Prob. 3ECh. R.2 - Prob. 4ECh. R.2 - Prob. 5ECh. R.2 - Prob. 6ECh. R.2 - Prob. 7ECh. R.2 - Prob. 8ECh. R.2 - Prob. 9ECh. R.2 - Prob. 10ECh. R.2 - Prob. 11ECh. R.2 - Prob. 12ECh. R.2 - Prob. 13ECh. R.2 - Prob. 14ECh. R.2 - Prob. 15ECh. R.2 - Prob. 16ECh. R.2 - Prob. 17ECh. R.2 - Prob. 18ECh. R.2 - Prob. 19ECh. R.2 - Prob. 20ECh. R.2 - Prob. 21ECh. R.2 - Prob. 22ECh. R.2 - Prob. 23ECh. R.2 - Prob. 24ECh. R.2 - Prob. 25ECh. R.2 - Prob. 26ECh. R.2 - Prob. 27ECh. R.2 - Prob. 28ECh. R.2 - Prob. 29ECh. R.2 - Prob. 30ECh. R.2 - Prob. 31ECh. R.2 - Prob. 32ECh. R.3 - YOUR TURN 1 Write in lowest terms .
Ch. R.3 - YOUR TURN 2 Perform each of the following...Ch. R.3 - Prob. 1ECh. R.3 - Prob. 2ECh. R.3 - Prob. 3ECh. R.3 - Prob. 4ECh. R.3 - Prob. 5ECh. R.3 - Prob. 6ECh. R.3 - Prob. 7ECh. R.3 - Prob. 8ECh. R.3 - Prob. 9ECh. R.3 - Prob. 10ECh. R.3 - Prob. 11ECh. R.3 - Prob. 12ECh. R.3 - Prob. 13ECh. R.3 - Prob. 14ECh. R.3 - Prob. 15ECh. R.3 - Prob. 16ECh. R.3 - Prob. 17ECh. R.3 - Prob. 18ECh. R.3 - Prob. 19ECh. R.3 - Perform the indicated operations.
20.
Ch. R.3 - Prob. 21ECh. R.3 - Prob. 22ECh. R.3 - Prob. 23ECh. R.3 - Prob. 24ECh. R.3 - Prob. 25ECh. R.3 - Prob. 26ECh. R.3 - Prob. 27ECh. R.3 - Prob. 28ECh. R.3 - Prob. 29ECh. R.3 - Prob. 30ECh. R.3 - Prob. 31ECh. R.3 - Prob. 32ECh. R.3 - Prob. 33ECh. R.3 - Prob. 34ECh. R.3 - Prob. 35ECh. R.3 - Prob. 36ECh. R.3 - Prob. 37ECh. R.3 - Prob. 38ECh. R.4 - YOUR TURN 1 Solve .
Ch. R.4 - Prob. 2YTCh. R.4 - Prob. 3YTCh. R.4 - Prob. 4YTCh. R.4 - Prob. 1ECh. R.4 - Prob. 2ECh. R.4 - Prob. 3ECh. R.4 - Prob. 4ECh. R.4 - Prob. 5ECh. R.4 - Prob. 6ECh. R.4 - Prob. 7ECh. R.4 - Prob. 8ECh. R.4 - Prob. 9ECh. R.4 - Prob. 10ECh. R.4 - Prob. 11ECh. R.4 - Prob. 12ECh. R.4 - Prob. 13ECh. R.4 - Prob. 14ECh. R.4 - Prob. 15ECh. R.4 - Prob. 16ECh. R.4 - Prob. 17ECh. R.4 - Prob. 18ECh. R.4 - Prob. 19ECh. R.4 - Prob. 20ECh. R.4 - Prob. 21ECh. R.4 - Prob. 22ECh. R.4 - Prob. 23ECh. R.4 - Prob. 24ECh. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Prob. 26ECh. R.4 - Prob. 27ECh. R.4 - Prob. 28ECh. R.4 - Prob. 29ECh. R.4 - Prob. 30ECh. R.4 - Prob. 31ECh. R.4 - Prob. 32ECh. R.4 - Prob. 33ECh. R.4 - Prob. 34ECh. R.4 - Prob. 35ECh. R.4 - Prob. 36ECh. R.4 - Prob. 37ECh. R.5 - YOUR TURN 1 Solve 3z – 2 > 5z + 7.
Ch. R.5 - YOUR TURN 2 Solve 3y2 16y + 12.
Ch. R.5 - Prob. 3YTCh. R.5 - Prob. 1ECh. R.5 - Write each expression in interval notation, Graph...Ch. R.5 - Prob. 3ECh. R.5 - Write each expression in interval notation, Graph...Ch. R.5 - Prob. 5ECh. R.5 - Prob. 6ECh. R.5 - Prob. 7ECh. R.5 - Prob. 8ECh. R.5 - Prob. 9ECh. R.5 - Using the variable x, write each interval as an...Ch. R.5 - Prob. 11ECh. R.5 - Using the variable x, write each interval as an...Ch. R.5 - Prob. 13ECh. R.5 - Prob. 14ECh. R.5 - Prob. 15ECh. R.5 - Solve each inequality and graph the...Ch. R.5 - Prob. 17ECh. R.5 - Prob. 18ECh. R.5 - Prob. 19ECh. R.5 - Solve each inequality and graph the...Ch. R.5 - Prob. 21ECh. R.5 - Prob. 22ECh. R.5 - Prob. 23ECh. R.5 - Solve each inequality and graph the...Ch. R.5 - Solve each inequality and graph the...Ch. R.5 - Prob. 26ECh. R.5 - Prob. 27ECh. R.5 - Solve each inequality. Graph each solution.
28.
Ch. R.5 - Prob. 29ECh. R.5 - Solve each inequality. Graph each solution.
30.
Ch. R.5 - Prob. 31ECh. R.5 - Solve each inequality. Graph each solution.
32.
Ch. R.5 - Prob. 33ECh. R.5 - Prob. 34ECh. R.5 - Prob. 35ECh. R.5 - Prob. 36ECh. R.5 - Prob. 37ECh. R.5 - Solve each inequality. Graph each solution.
38.
Ch. R.5 - Prob. 39ECh. R.5 - Solve each inequality. Graph each solution.
40.
Ch. R.5 - Prob. 41ECh. R.5 - Solve each inequality. Graph each solution.
42.
Ch. R.5 - Prob. 43ECh. R.5 - Prob. 44ECh. R.5 - Prob. 45ECh. R.5 - Solve each inequality.
46.
Ch. R.5 - Prob. 47ECh. R.5 - Prob. 48ECh. R.5 - Prob. 49ECh. R.5 - Prob. 50ECh. R.5 - Solve each inequality.
51.
Ch. R.5 - Solve each inequality.
52.
Ch. R.5 - Prob. 53ECh. R.5 - Prob. 54ECh. R.6 - YOUR TURN 1 Find
Ch. R.6 - YOUR TURN 2 Simplify
Ch. R.6 - Prob. 3YTCh. R.6 - Prob. 4YTCh. R.6 - Prob. 5YTCh. R.6 - Prob. 6YTCh. R.6 - Prob. 1ECh. R.6 - Evaluate each expression. Write all answers...Ch. R.6 - Prob. 3ECh. R.6 - Prob. 4ECh. R.6 - Prob. 5ECh. R.6 - Prob. 6ECh. R.6 - Prob. 7ECh. R.6 - Evaluate each expression. Write all answers...Ch. R.6 - Prob. 9ECh. R.6 - Prob. 10ECh. R.6 - Prob. 11ECh. R.6 - Simplify each expression. Assume that all...Ch. R.6 - Prob. 13ECh. R.6 - Prob. 14ECh. R.6 - Prob. 15ECh. R.6 - Prob. 16ECh. R.6 - Prob. 17ECh. R.6 - Simplify each expression. Assume that all...Ch. R.6 - Prob. 19ECh. R.6 - Simplify each expression. Assume that all...Ch. R.6 - Prob. 21ECh. R.6 - Prob. 22ECh. R.6 - Prob. 23ECh. R.6 - Simplify each expression, writing the answers as a...Ch. R.6 - Prob. 25ECh. R.6 - Prob. 26ECh. R.6 - Prob. 27ECh. R.6 - Prob. 28ECh. R.6 - Prob. 29ECh. R.6 - Write each number without exponents.
30.
Ch. R.6 - Prob. 31ECh. R.6 - Prob. 32ECh. R.6 - Prob. 33ECh. R.6 - Prob. 34ECh. R.6 - Prob. 35ECh. R.6 - Write each number without exponents.
36.
Ch. R.6 - Prob. 37ECh. R.6 - Prob. 38ECh. R.6 - Prob. 39ECh. R.6 - Simplify each expression. Write all answers with...Ch. R.6 - Prob. 41ECh. R.6 - Prob. 42ECh. R.6 - Prob. 43ECh. R.6 - Simplify each expression. Write all answers with...Ch. R.6 - Prob. 45ECh. R.6 - Prob. 46ECh. R.6 - Prob. 47ECh. R.6 - Prob. 48ECh. R.6 - Prob. 49ECh. R.6 - Simplify each expression. Write all answers with...Ch. R.6 - Prob. 51ECh. R.6 - Factor each expression.
52.
Ch. R.6 - Prob. 53ECh. R.6 - Prob. 54ECh. R.6 - Prob. 55ECh. R.6 - Factor each expression.
56.
Ch. R.7 - Prob. 1YTCh. R.7 - Prob. 2YTCh. R.7 - Prob. 3YTCh. R.7 - Prob. 1ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 3ECh. R.7 - Prob. 4ECh. R.7 - Prob. 5ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 7ECh. R.7 - Prob. 8ECh. R.7 - Prob. 9ECh. R.7 - Prob. 10ECh. R.7 - Prob. 11ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 13ECh. R.7 - Prob. 14ECh. R.7 - Prob. 15ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 17ECh. R.7 - Prob. 18ECh. R.7 - Prob. 19ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 21ECh. R.7 - Prob. 22ECh. R.7 - Prob. 23ECh. R.7 - Simplify each root, if possible.
24.
Ch. R.7 - Prob. 25ECh. R.7 - Prob. 26ECh. R.7 - Prob. 27ECh. R.7 - Prob. 28ECh. R.7 - Prob. 29ECh. R.7 - Prob. 30ECh. R.7 - Prob. 31ECh. R.7 - Prob. 32ECh. R.7 - Prob. 33ECh. R.7 - Prob. 34ECh. R.7 - Prob. 35ECh. R.7 - Prob. 36ECh. R.7 - Prob. 37ECh. R.7 - Prob. 38ECh. R.7 - Prob. 39ECh. R.7 - Prob. 40ECh. R.7 - Prob. 41ECh. R.7 - Prob. 42ECh. R.7 - Prob. 43ECh. R.7 - Prob. 44E
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