(a) For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

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Answer 1

Question

Chapter 9.6, Problem 20P

To determine

(a)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

To determine

(b)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

To determine

(c)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

To determine

(d)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

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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). =

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Answer 2

Question

Chapter 9.6, Problem 20P

To determine

(a)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

To determine

(b)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

To determine

(c)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

To determine

(d)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

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Answer 3

Question

Chapter 9.6, Problem 20P

To determine

(a)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

To determine

(b)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

To determine

(c)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

To determine

(d)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

Expert Solution & Answer

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See solution

Answer 4

Question

Chapter 9.6, Problem 20P

To determine

(a)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

To determine

(b)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

To determine

(c)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

To determine

(d)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

Expert Solution & Answer

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Answer 5

Chapter 9.6, Problem 20P

To determine

(a)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

To determine

(b)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

To determine

(c)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

To determine

(d)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

Answer 6

Chapter 9.6, Problem 20P

To determine

(a)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

Answer 7

Chapter 9.6, Problem 20P

To determine

(a)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

Answer 8

To determine

(b)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

Answer 9

To determine

(b)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

Answer 10

To determine

(c)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

Answer 11

To determine

(c)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

Answer 12

To determine

(d)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

Answer 13

To determine

(d)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 9.1 - Prob. 1P Ch. 9.1 - Prob. 2P Ch. 9.1 - Prob. 3P Ch. 9.1 - Prob. 4P Ch. 9.1 - Prob. 5P Ch. 9.1 - Prob. 6P Ch. 9.1 - Prob. 7P Ch. 9.1 - Prob. 8P Ch. 9.1 - Prob. 9P Ch. 9.1 - Prob. 10P

(a) For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

Solution Summary: The author explains how x and y grow exponentially, and how each specie inhibits the other’s growth.

Videos

(a)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

(b)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

(c)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

(d)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

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Chapter 9 Solutions

(a) For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

Solution Summary: The author explains how x and y grow exponentially, and how each specie inhibits the other’s growth.

Videos

(a) For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

(b) For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

(c) For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

(d) For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

Want to see the full answer?

Chapter 9 Solutions

(a)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

(b)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

(c)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.

(d)

For each system of differential equation in example 2, determine whether x increases or decreases and whether y increases or decreases when x = 2 and y = 2.