The fixed points of the iterated map x t + 1 = f ( x t ) where f ( x ) = x 2 and show that it has exactly two fixed points of which one is stable.

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Answer 1

Question

Chapter 12, Problem 12.22P

(a)

To determine

The fixed points of the iterated map xt+1=f(xt) where f(x)=x2 and show that it has exactly two fixed points of which one is stable.

(b)

To determine

Show that xt approaches the stable fixed point only if −1<x0<1.

(c)

To determine

Show that xt→∞ only if |x0|>1.

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Answer 2

Question

Chapter 12, Problem 12.22P

(a)

To determine

The fixed points of the iterated map xt+1=f(xt) where f(x)=x2 and show that it has exactly two fixed points of which one is stable.

(b)

To determine

Show that xt approaches the stable fixed point only if −1<x0<1.

(c)

To determine

Show that xt→∞ only if |x0|>1.

Expert Solution & Answer

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Answer 3

Question

Chapter 12, Problem 12.22P

(a)

To determine

The fixed points of the iterated map xt+1=f(xt) where f(x)=x2 and show that it has exactly two fixed points of which one is stable.

(b)

To determine

Show that xt approaches the stable fixed point only if −1<x0<1.

(c)

To determine

Show that xt→∞ only if |x0|>1.

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Answer 4

Question

Chapter 12, Problem 12.22P

(a)

To determine

The fixed points of the iterated map xt+1=f(xt) where f(x)=x2 and show that it has exactly two fixed points of which one is stable.

(b)

To determine

Show that xt approaches the stable fixed point only if −1<x0<1.

(c)

To determine

Show that xt→∞ only if |x0|>1.

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Answer 5

Chapter 12, Problem 12.22P

(a)

To determine

The fixed points of the iterated map xt+1=f(xt) where f(x)=x2 and show that it has exactly two fixed points of which one is stable.

(b)

To determine

Show that xt approaches the stable fixed point only if −1<x0<1.

(c)

To determine

Show that xt→∞ only if |x0|>1.

Answer 6

Chapter 12, Problem 12.22P

(a)

To determine

The fixed points of the iterated map xt+1=f(xt) where f(x)=x2 and show that it has exactly two fixed points of which one is stable.

Answer 7

Chapter 12, Problem 12.22P

(a)

To determine

The fixed points of the iterated map xt+1=f(xt) where f(x)=x2 and show that it has exactly two fixed points of which one is stable.

Answer 8

(b)

To determine

Show that xt approaches the stable fixed point only if −1<x0<1.

Answer 9

(b)

To determine

Show that xt approaches the stable fixed point only if −1<x0<1.

Answer 10

(c)

To determine

Show that xt→∞ only if |x0|>1.

Answer 11

(c)

To determine

Show that xt→∞ only if |x0|>1.

Answer 12

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Answer 13

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Answer 14

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Answer 15

Ch. 12 - Prob. 12.1P Ch. 12 - Prob. 12.2P Ch. 12 - Prob. 12.3P Ch. 12 - Prob. 12.4P Ch. 12 - Prob. 12.5P Ch. 12 - Prob. 12.11P Ch. 12 - Prob. 12.13P Ch. 12 - Prob. 12.16P Ch. 12 - Prob. 12.19P Ch. 12 - Prob. 12.20P

The fixed points of the iterated map x t + 1 = f ( x t ) where f ( x ) = x 2 and show that it has exactly two fixed points of which one is stable.

The fixed points of the iterated map xt+1=f(xt) where f(x)=x2 and show that it has exactly two fixed points of which one is stable.

Show that xt approaches the stable fixed point only if −1<x0<1.

Show that xt→∞ only if |x0|>1.

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Chapter 12 Solutions