a) Toprove: Why y = f ( x ) is an even function?

Question

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Answer 1

Question

Chapter 9.4, Problem 49E

To determine

a)

Toprove:

Why $y = f (x)$ is an even function?

To determine

b)

To prove:

$y = x f (x)$ is an odd function

To determine

c)

To prove:

$M_{y} = 0$

To determine

d)

To prove:Centre of mass of $R$ lies on the $y - axis$

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Symmetry Principle Let R be the region under the graph of y = f (x) over the interval [−a, a], where f (x) ≥ 0. Assume that R is symmetric with respect to the y-axis. (a) Explain why y = f (x) is even—that is, why f (x) = f (−x). (b) Show that y = xf (x) is an odd function. (c) Use (b) to prove that My = 0. (d) Prove that the COM of R lies on the y-axis (a similar argument applies to symmetry with respect to the x-axis).

Symmetry Principle Let R be the region under the graph of y = f (x) over the interval [−a, a], where f (x) ≥ 0. Assume that R is symmetric with respect to the y-axis.

1) Let f be the function defined by f(x) = 2^x and let g be defined by g(x) = 4rootx . The region R in the first quadrant is bounded by the graphs of f and g a) find the area of R. b) The region R is the base of a solid whose cross sections are squares perpendicular to the x-axis. Find the volume of this solid. c) The region R is revolves around the line x=4 to generate a solid. Find the volume of this solid.

Answer 2

Question

Chapter 9.4, Problem 49E

To determine

a)

Toprove:

Why $y = f (x)$ is an even function?

To determine

b)

To prove:

$y = x f (x)$ is an odd function

To determine

c)

To prove:

$M_{y} = 0$

To determine

d)

To prove:Centre of mass of $R$ lies on the $y - axis$

Expert Solution & Answer

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Answer 3

Question

Chapter 9.4, Problem 49E

To determine

a)

Toprove:

Why $y = f (x)$ is an even function?

To determine

b)

To prove:

$y = x f (x)$ is an odd function

To determine

c)

To prove:

$M_{y} = 0$

To determine

d)

To prove:Centre of mass of $R$ lies on the $y - axis$

Expert Solution & Answer

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See solution

Answer 4

Question

Chapter 9.4, Problem 49E

To determine

a)

Toprove:

Why $y = f (x)$ is an even function?

To determine

b)

To prove:

$y = x f (x)$ is an odd function

To determine

c)

To prove:

$M_{y} = 0$

To determine

d)

To prove:Centre of mass of $R$ lies on the $y - axis$

Expert Solution & Answer

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See solution

Answer 5

Chapter 9.4, Problem 49E

To determine

a)

Toprove:

Why $y = f (x)$ is an even function?

To determine

b)

To prove:

$y = x f (x)$ is an odd function

To determine

c)

To prove:

$M_{y} = 0$

To determine

d)

To prove:Centre of mass of $R$ lies on the $y - axis$

Answer 6

Chapter 9.4, Problem 49E

To determine

a)

Toprove:

Why $y = f (x)$ is an even function?

Answer 7

Chapter 9.4, Problem 49E

To determine

a)

Toprove:

Why $y = f (x)$ is an even function?

Answer 8

To determine

b)

To prove:

$y = x f (x)$ is an odd function

Answer 9

To determine

b)

To prove:

$y = x f (x)$ is an odd function

Answer 10

To determine

c)

To prove:

$M_{y} = 0$

Answer 11

To determine

c)

To prove:

$M_{y} = 0$

Answer 12

To determine

d)

To prove:Centre of mass of $R$ lies on the $y - axis$

Answer 13

To determine

d)

To prove:Centre of mass of $R$ lies on the $y - axis$

Answer 14

Expert Solution & Answer

Answer 15

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Answer 16

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Answer 17

Ch. 9.1 - Prob. 1PQ Ch. 9.1 - Prob. 2PQ Ch. 9.1 - Prob. 3PQ Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E

a) Toprove: Why y = f ( x ) is an even function?

Solution Summary: The author explains why y = f ( x ) is an even function.

Concept explainers

Videos

a)

Toprove:

Why $y = f (x)$ is an even function?

b)

To prove:

$y = x f (x)$ is an odd function

c)

To prove:

$M_{y} = 0$

d)

To prove:Centre of mass of $R$ lies on the $y - axis$

Want to see the full answer?

Chapter 9 Solutions

a) Toprove: Why y = f ( x ) is an even function?

Solution Summary: The author explains why y = f ( x ) is an even function.

Concept explainers

Videos

a) Toprove: Why y=f(x) is an even function?

b) To prove: y=xf(x) is an odd function

c) To prove: My=0

d) To prove:Centre of mass of R lies on the y−axis

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Chapter 9 Solutions

a)

Toprove:

Why $y = f (x)$ is an even function?

b)

To prove:

$y = x f (x)$ is an odd function

c)

To prove:

$M_{y} = 0$

d)

To prove:Centre of mass of $R$ lies on the $y - axis$