Calculus: An Applied Approach (Providence College: MTH 109)
9th Edition
ISBN: 9781285142616
Author: Ron Larson
Publisher: CENGAGE C
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Chapter A1, Problem 3CP
Checkpoint 3 Worked-out solution available at LarsonAppliedCalculus.com
Use the information in Example 3 to find the high and low production levels during the month of October, when the total cost of production varied from a high of $1500 to a low of $1000 per day.
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(7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz).
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(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 A1 Solutions
Calculus: An Applied Approach (Providence College: MTH 109)
Ch. A1 - Prob. 1CPCh. A1 - Prob. 2CPCh. A1 - Checkpoint 3 Worked-out solution available at...Ch. A1 - Prob. 1ECh. A1 - Prob. 2ECh. A1 - Prob. 3ECh. A1 - Prob. 4ECh. A1 - Prob. 5ECh. A1 - Prob. 6ECh. A1 - Prob. 7E
Ch. A1 - Prob. 8ECh. A1 - Prob. 9ECh. A1 - Prob. 10ECh. A1 - Prob. 11ECh. A1 - Prob. 12ECh. A1 - Prob. 13ECh. A1 - Prob. 14ECh. A1 - Prob. 15ECh. A1 - Prob. 16ECh. A1 - Prob. 17ECh. A1 - Prob. 18ECh. A1 - Prob. 19ECh. A1 - Prob. 20ECh. A1 - Prob. 21ECh. A1 - Prob. 22ECh. A1 - Prob. 23ECh. A1 - Prob. 24ECh. A1 - Prob. 25ECh. A1 - Prob. 26ECh. A1 - Prob. 27ECh. A1 - Prob. 28ECh. A1 - Prob. 29ECh. A1 - Writing Inequalities In Exercises 27-30, use...Ch. A1 - Prob. 31ECh. A1 - Prob. 32ECh. A1 - Profit The revenue for selling x units of a...Ch. A1 - Sales A doughnut shop sells a dozen doughnuts for...Ch. A1 - Prob. 35ECh. A1 - Prob. 36E
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