Use Green’s Theorem to evaluate the line integral and orient the curve counterclockwise unless otherwise indicated of given integral: ∮ C y 2 d x + x 2 d y , where C is boundary of the square − 1 ≤ x ≤ 1 , − 1 ≤ y ≤ 1

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Chapter 17.1, Problem 4E

To determine

Use Green’s Theorem to evaluate the line integral and orient the curve counterclockwise unless otherwise indicated of given integral:

∮Cy2dx+x2dy, where C is boundary of the square −1≤x≤1, −1≤y≤1

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Question 1. (10 points) A researcher is studying tumours in mice. The growth rate for the volume of the tumour V(t) in cm³ is given by dV = 1.45V(2 In(V+1)). dt (a) (4 pts) Find all the equilibria and determine their stability using the stability condition. (b) (2 pts) Draw the phase plot f(V) versus V where f(V) = V'. You may find it helpful to use Desmos or Wolfram Alpha to plot the graph of f(V) versus V (both are free to use online), or you can plot it by hand if you like. On the plot identify each equilibrium as stable or unstable. (c) (4 pts) Draw direction arrows for the case where the tumour starts at size 3cm³ and for the case where the tumour starts at size 9cm³. Explain in biological terms what happens to the size of each of these tumours at time progresses.

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Answer 2

Question

Chapter 17.1, Problem 4E

To determine

Use Green’s Theorem to evaluate the line integral and orient the curve counterclockwise unless otherwise indicated of given integral:

∮Cy2dx+x2dy, where C is boundary of the square −1≤x≤1, −1≤y≤1

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 3

Question

Chapter 17.1, Problem 4E

To determine

Use Green’s Theorem to evaluate the line integral and orient the curve counterclockwise unless otherwise indicated of given integral:

∮Cy2dx+x2dy, where C is boundary of the square −1≤x≤1, −1≤y≤1

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 4

Question

Chapter 17.1, Problem 4E

To determine

Use Green’s Theorem to evaluate the line integral and orient the curve counterclockwise unless otherwise indicated of given integral:

∮Cy2dx+x2dy, where C is boundary of the square −1≤x≤1, −1≤y≤1

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 17.1, Problem 4E

To determine

Use Green’s Theorem to evaluate the line integral and orient the curve counterclockwise unless otherwise indicated of given integral:

∮Cy2dx+x2dy, where C is boundary of the square −1≤x≤1, −1≤y≤1

Answer 6

Chapter 17.1, Problem 4E

To determine

Use Green’s Theorem to evaluate the line integral and orient the curve counterclockwise unless otherwise indicated of given integral:

∮Cy2dx+x2dy, where C is boundary of the square −1≤x≤1, −1≤y≤1

Answer 7

Chapter 17.1, Problem 4E

To determine

Use Green’s Theorem to evaluate the line integral and orient the curve counterclockwise unless otherwise indicated of given integral:

∮Cy2dx+x2dy, where C is boundary of the square −1≤x≤1, −1≤y≤1

Answer 8

Expert Solution & Answer

Answer 9

Expert Solution & Answer

Answer 10

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Answer 11

Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 5PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E

Use Green’s Theorem to evaluate the line integral and orient the curve counterclockwise unless otherwise indicated of given integral: ∮ C y 2 d x + x 2 d y , where C is boundary of the square − 1 ≤ x ≤ 1 , − 1 ≤ y ≤ 1

Solution Summary: The author explains how to evaluate the line integral and orient the curve counterclockwise unless otherwise indicated of given integral.

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Use Green’s Theorem to evaluate the line integral and orient the curve counterclockwise unless otherwise indicated of given integral:

∮Cy2dx+x2dy, where C is boundary of the square −1≤x≤1, −1≤y≤1

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Chapter 17 Solutions

Use Green’s Theorem to evaluate the line integral and orient the curve counterclockwise unless otherwise indicated of given integral: ∮ C y 2 d x + x 2 d y , where C is boundary of the square − 1 ≤ x ≤ 1 , − 1 ≤ y ≤ 1

Solution Summary: The author explains how to evaluate the line integral and orient the curve counterclockwise unless otherwise indicated of given integral.

Concept explainers

Videos

Use Green’s Theorem to evaluate the line integral and orient the curve counterclockwise unless otherwise indicated of given integral: ∮Cy2dx+x2dy, where C is boundary of the square −1≤x≤1, −1≤y≤1

Want to see the full answer?

Chapter 17 Solutions

Use Green’s Theorem to evaluate the line integral and orient the curve counterclockwise unless otherwise indicated of given integral:

∮Cy2dx+x2dy, where C is boundary of the square −1≤x≤1, −1≤y≤1