a. Explanation Given information: The function is f ( x ) = 1 σ 2 π − 1 2 ( x − μ σ ) 2 . Graph: to find the graph of the function, first plot some points and then joint them smoothly, x f ( x ) 0 1 3 0 − 3 0 Interpretation: from the above graph it can be observed that thefunction is increasing in the intervals [ − 3 , 0 ] ∪ [ 4.5 , 6 ] ∪ ... and decreasing in the intervals [ 0 , 3 ] ∪ [ 3 , 4.5 ] ∪ ... anf=d local maximum is 1 and occur at x = 0 . b. To determine To find: the value of ∫ − n n f ( x ) d x for n = 1 , 2 , 3 . Answer the value of integral is 1 for n = 1 , 2 , 3 . Explanation Given information: The integral is ∫ − n n f ( x ) d x . Calculation: to find the value, first substitute value then simplify, Since, ∫ − ∞ ∞ f ( x ) d x = 1 Thus, the value of integral, ∫ − 1 1 f ( x ) d x = 1 ∫ − 2 2 f ( x ) d x = 1 ∫ − 3 3 f ( x ) d x = 1 c. To determine To find: the a convincing argument that ∫ − ∞ ∞ f ( x ) d x = 1 . Answer 0 < f ( x ) < e − x 2 for x > 1 and for b > 1 , ∫ b ∞ e − x 2 d x → 0 as b → ∞ . Explanation Given information: The integral is ∫ − ∞ ∞ f ( x ) d x = 1 . Calculation: because, 0 < f ( x ) < e − x 2 for x > 1 and for b > 1 , ∫ b ∞ e − x 2 d x → 0 as b → ∞ .

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 9.4, Problem 56E

To determine

Tograph: the function and find the intervals on which function is increasing, decreasing and any local extreme values and where they occur.

Expert Solution

Explanation of Solution

Given information:

The function is $f(x)=1σ2π−12(x−μσ)2$ .

Graph: to find the graph of the function, first plot some points and then joint them smoothly,

$x$	$f(x)$
$0$	$1$
$3$	$0$
$−3$	$0$

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 9.4, Problem 56E

Interpretation: from the above graph it can be observed that thefunction is increasing in the intervals $[−3,0]∪[4.5,6]∪...$ and decreasing in the intervals $[0,3]∪[3,4.5]∪...$ anf=d local maximum is $1$ and occur at $x=0$ .

To determine

To find: the value of $∫−nnf(x)dx$ for $n=1,2,3$ .

Expert Solution

Answer to Problem 56E

the value of integral is $1$ for $n=1,2,3$ .

Explanation of Solution

Given information:

The integral is $∫−nnf(x)dx$ .

Calculation:to find the value, first substitute value then simplify,

Since, $∫−∞∞f(x)dx=1$

Thus, the value of integral,

$∫−11f(x)dx=1∫−22f(x)dx=1∫−33f(x)dx=1$

To determine

To find: the a convincing argument that $∫−∞∞f(x)dx=1$ .

Expert Solution

Answer to Problem 56E

$0<f(x)<e−x2$ for $x>1$ and for $b>1$ ,

$∫b∞e−x2dx→0$ as $b→∞$ .

Explanation of Solution

Given information:

The integral is $∫−∞∞f(x)dx=1$ .

Calculation: because,

$0<f(x)<e−x2$ for $x>1$ and for $b>1$ ,

$∫b∞e−x2dx→0$ as $b→∞$ .

Chapter 9.4, Problem 55E

Chapter 9.4, Problem 57E

Chapter 9 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 9.1 - Prob. 1QR Ch. 9.1 - Prob. 2QR Ch. 9.1 - Prob. 3QR Ch. 9.1 - Prob. 4QR Ch. 9.1 - Prob. 5QR Ch. 9.1 - Prob. 6QR Ch. 9.1 - Prob. 7QR Ch. 9.1 - Prob. 8QR Ch. 9.1 - Prob. 9QR Ch. 9.1 - Prob. 10QR

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 Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E Ch. 9.1 - Prob. 11E Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - Prob. 15E Ch. 9.1 - Prob. 16E Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - Prob. 20E Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - Prob. 23E Ch. 9.1 - Prob. 24E Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - Prob. 28E Ch. 9.1 - Prob. 29E Ch. 9.1 - Prob. 30E Ch. 9.1 - Prob. 31E Ch. 9.1 - Prob. 32E Ch. 9.1 - Prob. 33E Ch. 9.1 - Prob. 34E Ch. 9.1 - Prob. 35E Ch. 9.1 - Prob. 36E Ch. 9.1 - Prob. 37E Ch. 9.1 - Prob. 38E Ch. 9.1 - Prob. 39E Ch. 9.1 - Prob. 40E Ch. 9.1 - Prob. 41E Ch. 9.1 - Prob. 42E Ch. 9.1 - Prob. 43E Ch. 9.1 - Prob. 44E Ch. 9.1 - Prob. 45E Ch. 9.1 - Prob. 46E Ch. 9.1 - Prob. 47E Ch. 9.1 - Prob. 48E Ch. 9.1 - Prob. 49E Ch. 9.1 - Prob. 50E Ch. 9.1 - 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