(a) To find: The Equilibrium point of the given equation.

Question

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Answer 1

Question

Chapter 14.3, Problem 15E

To determine

(a)

To find:

The Equilibrium point of the given equation.

To determine

(b)

To find:

The value of the derivative of the function at the equilibrium points.

To determine

(c)

The stability of equilibrium points tells about each of the equilibrium points.

To determine

(d)

To find:

The next five values of the sequence and determine whether the equilibrium points are stable or unstable.

To determine

(e)

To find:

The behavior of the successive iterations found part d.

To determine

(f)

To find:

The behavior found in part d relates to the results from part c.

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Exercise 2. Obtain expressions for all first and second derivatives of the function of two variables f(x) = x + x₁x₂ + (1+x₂)². Evaluate these derivatives at x = 0 and show that G(0) is not positive definite. Exercise 3. Find and verify the type of stationary points for the following functions: a. f(x) = x² + 4x2 - 4x₁ - 8x₂ b. f(x) = x² + 2x² + 4x₁ + 4x₂ c. f(x) = 2x² - 4x² d. f(x) = 2x²-3x² - 6x₁x2(x2-x₁ - 1) e. f(x) = (x₂-x²)² - x²

Exercise 2. Obtain expressions for all first and second derivatives of the function of two variables f(x) = x₁ + x₁x₂ + (1+x₂)². Evaluate these derivatives at x = 0 and show that G(0) is not positive definite. Exercise 3. Find and verify the type of stationary points for the following functions: a. f(x) = x² + 4x² - 4x₁ - 8x₂ b. f(x) = x² + 2x² + 4x₁ + 4x₂ c. f(x) = 2x² - 4x²/ d. f(x) = 2x²-3x² - 6x₁x2(x₂-x₁ - 1) e. f(x) = (x₂-x²)² - x²

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Answer 2

Question

Chapter 14.3, Problem 15E

To determine

(a)

To find:

The Equilibrium point of the given equation.

To determine

(b)

To find:

The value of the derivative of the function at the equilibrium points.

To determine

(c)

The stability of equilibrium points tells about each of the equilibrium points.

To determine

(d)

To find:

The next five values of the sequence and determine whether the equilibrium points are stable or unstable.

To determine

(e)

To find:

The behavior of the successive iterations found part d.

To determine

(f)

To find:

The behavior found in part d relates to the results from part c.

Expert Solution & Answer

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Answer 3

Question

Chapter 14.3, Problem 15E

To determine

(a)

To find:

The Equilibrium point of the given equation.

To determine

(b)

To find:

The value of the derivative of the function at the equilibrium points.

To determine

(c)

The stability of equilibrium points tells about each of the equilibrium points.

To determine

(d)

To find:

The next five values of the sequence and determine whether the equilibrium points are stable or unstable.

To determine

(e)

To find:

The behavior of the successive iterations found part d.

To determine

(f)

To find:

The behavior found in part d relates to the results from part c.

Expert Solution & Answer

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Answer 4

Question

Chapter 14.3, Problem 15E

To determine

(a)

To find:

The Equilibrium point of the given equation.

To determine

(b)

To find:

The value of the derivative of the function at the equilibrium points.

To determine

(c)

The stability of equilibrium points tells about each of the equilibrium points.

To determine

(d)

To find:

The next five values of the sequence and determine whether the equilibrium points are stable or unstable.

To determine

(e)

To find:

The behavior of the successive iterations found part d.

To determine

(f)

To find:

The behavior found in part d relates to the results from part c.

Expert Solution & Answer

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Answer 5

Chapter 14.3, Problem 15E

To determine

(a)

To find:

The Equilibrium point of the given equation.

To determine

(b)

To find:

The value of the derivative of the function at the equilibrium points.

To determine

(c)

The stability of equilibrium points tells about each of the equilibrium points.

To determine

(d)

To find:

The next five values of the sequence and determine whether the equilibrium points are stable or unstable.

To determine

(e)

To find:

The behavior of the successive iterations found part d.

To determine

(f)

To find:

The behavior found in part d relates to the results from part c.

Answer 6

Chapter 14.3, Problem 15E

To determine

(a)

To find:

The Equilibrium point of the given equation.

Answer 7

Chapter 14.3, Problem 15E

To determine

(a)

To find:

The Equilibrium point of the given equation.

Answer 8

To determine

(b)

To find:

The value of the derivative of the function at the equilibrium points.

Answer 9

To determine

(b)

To find:

The value of the derivative of the function at the equilibrium points.

Answer 10

To determine

(c)

The stability of equilibrium points tells about each of the equilibrium points.

Answer 11

To determine

(c)

The stability of equilibrium points tells about each of the equilibrium points.

Answer 12

To determine

(d)

To find:

The next five values of the sequence and determine whether the equilibrium points are stable or unstable.

Answer 13

To determine

(d)

To find:

The next five values of the sequence and determine whether the equilibrium points are stable or unstable.

Answer 14

To determine

(e)

To find:

The behavior of the successive iterations found part d.

Answer 15

To determine

(e)

To find:

The behavior of the successive iterations found part d.

Answer 16

To determine

(f)

To find:

The behavior found in part d relates to the results from part c.

Answer 17

To determine

(f)

To find:

The behavior found in part d relates to the results from part c.

Answer 18

Expert Solution & Answer

Answer 19

Expert Solution & Answer

Answer 20

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Answer 21

Ch. 14.1 - YOUR TURN 1 Find the first four terms of the...Ch. 14.1 - Prob. 2YT Ch. 14.1 - Prob. 3YT Ch. 14.1 - Prob. 4YT Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E Ch. 14.1 - Prob. 6E

(a) To find: The Equilibrium point of the given equation.

Solution Summary: The author explains how to find the equilibrium point of the given equation by equating the function to x and finding the solution.

Concept explainers

Videos

(a)

To find:

The Equilibrium point of the given equation.

(b)

To find:

The value of the derivative of the function at the equilibrium points.

(c)

The stability of equilibrium points tells about each of the equilibrium points.

(d)

To find:

The next five values of the sequence and determine whether the equilibrium points are stable or unstable.

(e)

To find:

The behavior of the successive iterations found part d.

(f)

To find:

The behavior found in part d relates to the results from part c.

Want to see the full answer?

Chapter 14 Solutions

(a) To find: The Equilibrium point of the given equation.

Solution Summary: The author explains how to find the equilibrium point of the given equation by equating the function to x and finding the solution.

Concept explainers

Videos

(a) To find: The Equilibrium point of the given equation.

(b) To find: The value of the derivative of the function at the equilibrium points.

(c) The stability of equilibrium points tells about each of the equilibrium points.

(d) To find: The next five values of the sequence and determine whether the equilibrium points are stable or unstable.

(e) To find: The behavior of the successive iterations found part d.

(f) To find: The behavior found in part d relates to the results from part c.

Want to see the full answer?

Chapter 14 Solutions

(a)

To find:

The Equilibrium point of the given equation.

(b)

To find:

The value of the derivative of the function at the equilibrium points.

(c)

The stability of equilibrium points tells about each of the equilibrium points.

(d)

To find:

The next five values of the sequence and determine whether the equilibrium points are stable or unstable.

(e)

To find:

The behavior of the successive iterations found part d.

(f)

To find:

The behavior found in part d relates to the results from part c.