(a) To prove: That the graphs of the two limacons are exactly the same for both b and − b .

Question

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Answer 1

Question

Chapter 12.3, Problem 64E

To determine

(a)

To prove:

That the graphs of the two limacons are exactly the same for both $b and - b$ .

To determine

(b)

To plot:

The limacon for the given values of b and describe how it changes the shape.

To determine

(c)

To plot:

The limacon for the given values of b and describe how it changes the shape.

To determine

(d)

To show:

$\frac{d y}{d x} = - (\frac{b \cos θ + \cos 2 θ}{b + 2 \cos θ}) \csc θ$

To determine

(e)

The points where tangent line is vertical.

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Answer 2

Question

Chapter 12.3, Problem 64E

To determine

(a)

To prove:

That the graphs of the two limacons are exactly the same for both $b and - b$ .

To determine

(b)

To plot:

The limacon for the given values of b and describe how it changes the shape.

To determine

(c)

To plot:

The limacon for the given values of b and describe how it changes the shape.

To determine

(d)

To show:

$\frac{d y}{d x} = - (\frac{b \cos θ + \cos 2 θ}{b + 2 \cos θ}) \csc θ$

To determine

(e)

The points where tangent line is vertical.

Expert Solution & Answer

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Answer 3

Question

Chapter 12.3, Problem 64E

To determine

(a)

To prove:

That the graphs of the two limacons are exactly the same for both $b and - b$ .

To determine

(b)

To plot:

The limacon for the given values of b and describe how it changes the shape.

To determine

(c)

To plot:

The limacon for the given values of b and describe how it changes the shape.

To determine

(d)

To show:

$\frac{d y}{d x} = - (\frac{b \cos θ + \cos 2 θ}{b + 2 \cos θ}) \csc θ$

To determine

(e)

The points where tangent line is vertical.

Expert Solution & Answer

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Answer 4

Question

Chapter 12.3, Problem 64E

To determine

(a)

To prove:

That the graphs of the two limacons are exactly the same for both $b and - b$ .

To determine

(b)

To plot:

The limacon for the given values of b and describe how it changes the shape.

To determine

(c)

To plot:

The limacon for the given values of b and describe how it changes the shape.

To determine

(d)

To show:

$\frac{d y}{d x} = - (\frac{b \cos θ + \cos 2 θ}{b + 2 \cos θ}) \csc θ$

To determine

(e)

The points where tangent line is vertical.

Expert Solution & Answer

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Answer 5

Chapter 12.3, Problem 64E

To determine

(a)

To prove:

That the graphs of the two limacons are exactly the same for both $b and - b$ .

To determine

(b)

To plot:

The limacon for the given values of b and describe how it changes the shape.

To determine

(c)

To plot:

The limacon for the given values of b and describe how it changes the shape.

To determine

(d)

To show:

$\frac{d y}{d x} = - (\frac{b \cos θ + \cos 2 θ}{b + 2 \cos θ}) \csc θ$

To determine

(e)

The points where tangent line is vertical.

Answer 6

Chapter 12.3, Problem 64E

To determine

(a)

To prove:

That the graphs of the two limacons are exactly the same for both $b and - b$ .

Answer 7

Chapter 12.3, Problem 64E

To determine

(a)

To prove:

That the graphs of the two limacons are exactly the same for both $b and - b$ .

Answer 8

To determine

(b)

To plot:

The limacon for the given values of b and describe how it changes the shape.

Answer 9

To determine

(b)

To plot:

The limacon for the given values of b and describe how it changes the shape.

Answer 10

To determine

(c)

To plot:

The limacon for the given values of b and describe how it changes the shape.

Answer 11

To determine

(c)

To plot:

The limacon for the given values of b and describe how it changes the shape.

Answer 12

To determine

(d)

To show:

$\frac{d y}{d x} = - (\frac{b \cos θ + \cos 2 θ}{b + 2 \cos θ}) \csc θ$

Answer 13

To determine

(d)

To show:

$\frac{d y}{d x} = - (\frac{b \cos θ + \cos 2 θ}{b + 2 \cos θ}) \csc θ$

Answer 14

To determine

(e)

The points where tangent line is vertical.

Answer 15

To determine

(e)

The points where tangent line is vertical.

Answer 16

Expert Solution & Answer

Answer 17

Expert Solution & Answer

Answer 18

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Answer 19

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

(a) To prove: That the graphs of the two limacons are exactly the same for both b and − b .

Solution Summary: The author illustrates how the graph of r = b + cos is identical for both the polar equations, and explains how it changes the shape.

Videos

(a)

To prove:

That the graphs of the two limacons are exactly the same for both $b and - b$ .

(b)

To plot:

The limacon for the given values of b and describe how it changes the shape.

(c)

To plot:

The limacon for the given values of b and describe how it changes the shape.

(d)

To show:

$\frac{d y}{d x} = - (\frac{b \cos θ + \cos 2 θ}{b + 2 \cos θ}) \csc θ$

(e)

The points where tangent line is vertical.

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Chapter 12 Solutions

(a) To prove: That the graphs of the two limacons are exactly the same for both b and − b .

Solution Summary: The author illustrates how the graph of r = b + cos is identical for both the polar equations, and explains how it changes the shape.

Videos

(a) To prove: That the graphs of the two limacons are exactly the same for both b and −b.

(b) To plot: The limacon for the given values of b and describe how it changes the shape.

(c) To plot: The limacon for the given values of b and describe how it changes the shape.

(d) To show: dydx=−(bcosθ+cos2θb+2cosθ)cscθ

(e) The points where tangent line is vertical.

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Chapter 12 Solutions

(a)

To prove:

That the graphs of the two limacons are exactly the same for both $b and - b$ .

(b)

To plot:

The limacon for the given values of b and describe how it changes the shape.

(c)

To plot:

The limacon for the given values of b and describe how it changes the shape.

(d)

To show:

$\frac{d y}{d x} = - (\frac{b \cos θ + \cos 2 θ}{b + 2 \cos θ}) \csc θ$

(e)

The points where tangent line is vertical.