Precalculus
Precalculus
9th Edition
ISBN: 9780321716835
Author: Michael Sullivan
Publisher: Addison Wesley
Question
Book Icon
Chapter 14.5, Problem 17AYU
To determine

To solve: The function ƒ( x ) =  1 x is defined on the interval [ 1, 5 ] ,

a. Graph f ,

indicating the area A under f from 1 to 5.

Expert Solution
Check Mark

Answer to Problem 17AYU

a.

Precalculus, Chapter 14.5, Problem 17AYU , additional homework tip  1

Explanation of Solution

Given:

The function ƒ( x ) =  1 x is defined on the interval [ 1, 5 ]

ƒ( 1 ) = 1; ƒ( 3 2 ) =  2 3 ; ƒ( 2 ) =  1 2 ; ƒ( 5 2 ) =  2 5 ; ƒ( 3 ) =  1 3 ; ƒ( 7 2 ) =  2 7 ; ƒ( 4 ) =  1 4 ; ƒ( 9 2 ) =  2 9

Calculation:

a. Graph ƒ( x ) =  1 x

Precalculus, Chapter 14.5, Problem 17AYU , additional homework tip  2

To determine

To solve: The function ƒ( x ) =  1 x is defined on the interval [ 1, 5 ] ,

b. Approximate the area A by Partition [ 1, 5 ] into four subintervals of equal length and choose u as the left endpoint of each subinterval.

Expert Solution
Check Mark

Answer to Problem 17AYU

b. 25 12

Explanation of Solution

Given:

The function ƒ( x ) =  1 x is defined on the interval [ 1, 5 ]

ƒ( 1 ) = 1; ƒ( 3 2 ) =  2 3 ; ƒ( 2 ) =  1 2 ; ƒ( 5 2 ) =  2 5 ; ƒ( 3 ) =  1 3 ; ƒ( 7 2 ) =  2 7 ; ƒ( 4 ) =  1 4 ; ƒ( 9 2 ) =  2 9

Calculation:

b. Partition [ 1, 5 ] into four subintervals of equal length 1 and choose u as the left endpoint of each subinterval.

The area A is approximated as

A = f( 1 )1 + f( 2 )1 + f( 3 )1 + f( 4 )1

= 1( 1 ) +  1 2 ( 1 ) +  1 3 ( 1 ) +  1 4  ( 1 )

= 1 +  1 2  +  1 3  +  1 4  =  12 + 6 + 4 + 3 12

=  25 12

To determine

To solve: The function ƒ( x ) =  1 x is defined on the interval [ 1, 5 ] ,

c. Approximate the area A by Partition [ 1, 5 ] into eight subintervals of equal length and choose u as the left endpoint of each subinterval.

Expert Solution
Check Mark

Answer to Problem 17AYU

c. 4609 2520

Explanation of Solution

Given:

The function ƒ( x ) =  1 x is defined on the interval [ 1, 5 ]

ƒ( 1 ) = 1; ƒ( 3 2 ) =  2 3 ; ƒ( 2 ) =  1 2 ; ƒ( 5 2 ) =  2 5 ; ƒ( 3 ) =  1 3 ; ƒ( 7 2 ) =  2 7 ; ƒ( 4 ) =  1 4 ; ƒ( 9 2 ) =  2 9

Calculation:

c. Partition [ 1, 5 ] into eight subintervals of equal length 1 2 and choose u as the left endpoint of each subinterval.

The area A is approximated as

A = f( 1 )( 1 2 ) + f( 3 2 )( 1 2 ) + f( 2 )( 1 2 ) + f( 5 2 )( 1 2 ) + f( 3 )( 1 2 ) + f( 7 2  ) 1 2  + f( 4 )( 1 2 ) + f( 9 2 )( 1 2 )

= 1( 1 2 ) + ( 2 3 )( 1 2 ) +  1 2 ( 1 2 ) + ( 2 5 )( 1 2 ) +  1 3  ( 1 2 ) +  2 7 ( 1 2 ) +  1 4 ( 1 2 ) + ( 9 2 )( 1 2 )

=  1 2  +  1 3  +  1 4  +  1 5  +  1 6  +  1 7  +  1 8  +  1 9

=  1260 + 840 + 630 + 504 + 420 + 360 + 315 + 280 2520  =  4609 2520

To determine

To solve: The function ƒ( x ) =  1 x is defined on the interval [ 1, 5 ] ,

d. Express the area A as an integral.

Expert Solution
Check Mark

Answer to Problem 17AYU

d. 1 5 1 x dx

Explanation of Solution

Given:

The function ƒ( x ) =  1 x is defined on the interval [ 1, 5 ]

ƒ( 1 ) = 1; ƒ( 3 2 ) =  2 3 ; ƒ( 2 ) =  1 2 ; ƒ( 5 2 ) =  2 5 ; ƒ( 3 ) =  1 3 ; ƒ( 7 2 ) =  2 7 ; ƒ( 4 ) =  1 4 ; ƒ( 9 2 ) =  2 9  

Calculation:

d. Express the area A as an integral

The area A as an integral is 1 5 1 x dx

To determine

To solve: The function ƒ( x ) =  1 x is defined on the interval [ 1, 5 ] ,

e. Use a graphing utility to approximate the integral.

Expert Solution
Check Mark

Answer to Problem 17AYU

e. 1.609

Explanation of Solution

Given:

The function ƒ( x ) =  1 x is defined on the interval [ 1, 5 ]

ƒ( 1 ) = 1; ƒ( 3 2 ) =  2 3 ; ƒ( 2 ) =  1 2 ; ƒ( 5 2 ) =  2 5 ; ƒ( 3 ) =  1 3 ; ƒ( 7 2 ) =  2 7 ; ƒ( 4 ) =  1 4 ; ƒ( 9 2 ) =  2 9  

Calculation:

e. Use a graphing utility to approximate the integral.

That is evaluate the integral.

The value of the integral 1 5 1 x dx is 1.609 ,

so the area under the graph of ƒ from 1 to 5 is 1.609 .

Chapter 14 Solutions

Precalculus

Ch. 14.1 - Prob. 11AYUCh. 14.1 - Prob. 12AYUCh. 14.1 - Prob. 13AYUCh. 14.1 - Prob. 14AYUCh. 14.1 - Prob. 15AYUCh. 14.1 - Prob. 16AYUCh. 14.1 - In Problems 17-22, use the graph shown to...Ch. 14.1 - In Problems 17-22, use the graph shown to...Ch. 14.1 - In Problems 17-22, use the graph shown to...Ch. 14.1 - Prob. 20AYUCh. 14.1 - In Problems 17-22, use the graph shown to...Ch. 14.1 - Prob. 22AYUCh. 14.1 - Prob. 23AYUCh. 14.1 - Prob. 24AYUCh. 14.1 - Prob. 25AYUCh. 14.1 - Prob. 26AYUCh. 14.1 - In Problems 23-42, graph each function. Use the...Ch. 14.1 - Prob. 28AYUCh. 14.1 - Prob. 29AYUCh. 14.1 - Prob. 30AYUCh. 14.1 - In Problems 23-42, graph each function. Use the...Ch. 14.1 - Prob. 32AYUCh. 14.1 - Prob. 33AYUCh. 14.1 - Prob. 34AYUCh. 14.1 - In Problems 23-42, graph each function. Use the...Ch. 14.1 - In Problems 23-42, graph each function. Use the...Ch. 14.1 - In Problems 23-42, graph each function. Use the...Ch. 14.1 - Prob. 38AYUCh. 14.1 - Prob. 39AYUCh. 14.1 - Prob. 40AYUCh. 14.1 - Prob. 41AYUCh. 14.1 - Prob. 42AYUCh. 14.1 - In Problems 43-48, use a graphing utility to find...Ch. 14.1 - Prob. 44AYUCh. 14.1 - Prob. 45AYUCh. 14.1 - Prob. 46AYUCh. 14.1 - Prob. 47AYUCh. 14.1 - In Problems 43-48, use a graphing utility to find...Ch. 14.2 - Prob. 1AYUCh. 14.2 - Prob. 2AYUCh. 14.2 - Prob. 3AYUCh. 14.2 - Prob. 4AYUCh. 14.2 - Prob. 5AYUCh. 14.2 - Prob. 6AYUCh. 14.2 - Prob. 7AYUCh. 14.2 - Prob. 8AYUCh. 14.2 - Prob. 9AYUCh. 14.2 - Prob. 10AYUCh. 14.2 - Prob. 11AYUCh. 14.2 - Prob. 12AYUCh. 14.2 - Prob. 13AYUCh. 14.2 - Prob. 14AYUCh. 14.2 - Prob. 15AYUCh. 14.2 - Prob. 16AYUCh. 14.2 - Prob. 17AYUCh. 14.2 - Prob. 18AYUCh. 14.2 - Prob. 19AYUCh. 14.2 - Prob. 20AYUCh. 14.2 - Prob. 21AYUCh. 14.2 - Prob. 22AYUCh. 14.2 - Prob. 23AYUCh. 14.2 - Prob. 24AYUCh. 14.2 - Prob. 25AYUCh. 14.2 - Prob. 26AYUCh. 14.2 - Prob. 27AYUCh. 14.2 - Prob. 28AYUCh. 14.2 - Prob. 29AYUCh. 14.2 - Prob. 30AYUCh. 14.2 - Prob. 31AYUCh. 14.2 - Prob. 32AYUCh. 14.2 - Prob. 33AYUCh. 14.2 - Prob. 34AYUCh. 14.2 - Prob. 35AYUCh. 14.2 - Prob. 36AYUCh. 14.2 - Prob. 37AYUCh. 14.2 - Prob. 38AYUCh. 14.2 - Prob. 39AYUCh. 14.2 - Prob. 40AYUCh. 14.2 - Prob. 41AYUCh. 14.2 - Prob. 42AYUCh. 14.2 - In Problems 43-52, find the limit as x approaches...Ch. 14.2 - Prob. 44AYUCh. 14.2 - Prob. 45AYUCh. 14.2 - Prob. 46AYUCh. 14.2 - Prob. 47AYUCh. 14.2 - In Problems 43-52, find the limit as x approaches...Ch. 14.2 - Prob. 49AYUCh. 14.2 - Prob. 50AYUCh. 14.2 - Prob. 51AYUCh. 14.2 - Prob. 52AYUCh. 14.2 - In problems 53-56, use the properties of limits...Ch. 14.2 - Prob. 54AYUCh. 14.2 - Prob. 55AYUCh. 14.2 - In problems 53-56, use the properties of limits...Ch. 14.3 - For the function f( x )={ x 2 ifx0 x+1if0x2...Ch. 14.3 - Prob. 2AYUCh. 14.3 - Prob. 3AYUCh. 14.3 - Prob. 4AYUCh. 14.3 - Prob. 5AYUCh. 14.3 - Prob. 6AYUCh. 14.3 - Prob. 7AYUCh. 14.3 - Prob. 8AYUCh. 14.3 - Prob. 9AYUCh. 14.3 - Prob. 10AYUCh. 14.3 - Prob. 11AYUCh. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - Prob. 14AYUCh. 14.3 - Prob. 15AYUCh. 14.3 - Prob. 16AYUCh. 14.3 - Prob. 17AYUCh. 14.3 - Prob. 18AYUCh. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - Prob. 20AYUCh. 14.3 - Find lim x 4 f( x ) .Ch. 14.3 - Prob. 22AYUCh. 14.3 - Find lim x 2 f( x ) .Ch. 14.3 - Prob. 24AYUCh. 14.3 - Does lim x4 f( x ) exist? If it does, what is it?Ch. 14.3 - Prob. 26AYUCh. 14.3 - Is f continuous at 4 ?Ch. 14.3 - Prob. 28AYUCh. 14.3 - Is f continuous at 0?Ch. 14.3 - Prob. 30AYUCh. 14.3 - Is f continuous at 4?Ch. 14.3 - Prob. 32AYUCh. 14.3 - Prob. 33AYUCh. 14.3 - Prob. 34AYUCh. 14.3 - Prob. 35AYUCh. 14.3 - Prob. 36AYUCh. 14.3 - Prob. 37AYUCh. 14.3 - Prob. 38AYUCh. 14.3 - lim x 2 + x 2 4 x2Ch. 14.3 - lim x 1 x 3 x x1Ch. 14.3 - lim x 1 x 2 1 x 3 +1Ch. 14.3 - Prob. 42AYUCh. 14.3 - Prob. 43AYUCh. 14.3 - Prob. 44AYUCh. 14.3 - Prob. 45AYUCh. 14.3 - Prob. 46AYUCh. 14.3 - Prob. 47AYUCh. 14.3 - Prob. 48AYUCh. 14.3 - f( x )= x+3 x3 c=3Ch. 14.3 - Prob. 50AYUCh. 14.3 - Prob. 51AYUCh. 14.3 - Prob. 52AYUCh. 14.3 - Prob. 53AYUCh. 14.3 - Prob. 54AYUCh. 14.3 - Prob. 55AYUCh. 14.3 - Prob. 56AYUCh. 14.3 - f( x )={ x 3 1 x 2 1 ifx1 2ifx=1 3 x+1 ifx1 c=1Ch. 14.3 - Prob. 58AYUCh. 14.3 - Prob. 59AYUCh. 14.3 - Prob. 60AYUCh. 14.3 - Prob. 61AYUCh. 14.3 - Prob. 62AYUCh. 14.3 - Prob. 63AYUCh. 14.3 - Prob. 64AYUCh. 14.3 - Prob. 65AYUCh. 14.3 - Prob. 66AYUCh. 14.3 - Prob. 67AYUCh. 14.3 - Prob. 68AYUCh. 14.3 - f( x )= 2x+5 x 2 4Ch. 14.3 - Prob. 70AYUCh. 14.3 - Prob. 71AYUCh. 14.3 - Prob. 72AYUCh. 14.3 - Prob. 73AYUCh. 14.3 - Prob. 74AYUCh. 14.3 - Prob. 75AYUCh. 14.3 - Prob. 76AYUCh. 14.3 - Prob. 77AYUCh. 14.3 - Prob. 78AYUCh. 14.3 - Prob. 79AYUCh. 14.3 - Prob. 80AYUCh. 14.3 - Prob. 81AYUCh. 14.3 - Prob. 82AYUCh. 14.3 - Prob. 83AYUCh. 14.3 - Prob. 84AYUCh. 14.3 - Prob. 85AYUCh. 14.3 - Prob. 86AYUCh. 14.3 - Prob. 87AYUCh. 14.3 - Prob. 88AYUCh. 14.3 - Prob. 89AYUCh. 14.3 - Prob. 90AYUCh. 14.4 - Prob. 1AYUCh. 14.4 - Prob. 2AYUCh. 14.4 - Prob. 3AYUCh. 14.4 - lim xc f( x )f( c ) xc exists, it is called the...Ch. 14.4 - Prob. 5AYUCh. 14.4 - Prob. 6AYUCh. 14.4 - Prob. 7AYUCh. 14.4 - Prob. 8AYUCh. 14.4 - Prob. 9AYUCh. 14.4 - f( x )=2x+1 at ( 1,3 )Ch. 14.4 - Prob. 11AYUCh. 14.4 - Prob. 12AYUCh. 14.4 - Prob. 13AYUCh. 14.4 - Prob. 14AYUCh. 14.4 - Prob. 15AYUCh. 14.4 - Prob. 16AYUCh. 14.4 - Prob. 17AYUCh. 14.4 - Prob. 18AYUCh. 14.4 - Prob. 19AYUCh. 14.4 - Prob. 20AYUCh. 14.4 - Prob. 21AYUCh. 14.4 - Prob. 22AYUCh. 14.4 - Prob. 23AYUCh. 14.4 - Prob. 24AYUCh. 14.4 - Prob. 25AYUCh. 14.4 - Prob. 26AYUCh. 14.4 - Prob. 27AYUCh. 14.4 - Prob. 28AYUCh. 14.4 - Prob. 29AYUCh. 14.4 - Prob. 30AYUCh. 14.4 - Prob. 31AYUCh. 14.4 - Prob. 32AYUCh. 14.4 - Prob. 33AYUCh. 14.4 - Prob. 34AYUCh. 14.4 - Prob. 35AYUCh. 14.4 - Prob. 36AYUCh. 14.4 - Prob. 37AYUCh. 14.4 - Prob. 38AYUCh. 14.4 - Prob. 39AYUCh. 14.4 - Prob. 40AYUCh. 14.4 - Prob. 41AYUCh. 14.4 - Prob. 42AYUCh. 14.4 - Prob. 43AYUCh. 14.4 - Prob. 44AYUCh. 14.4 - Prob. 45AYUCh. 14.4 - Prob. 46AYUCh. 14.4 - Prob. 47AYUCh. 14.4 - Prob. 48AYUCh. 14.4 - Instantaneous Velocity on the Moon Neil Armstrong...Ch. 14.4 - Prob. 50AYUCh. 14.5 - In Problems 29-32, find the first five terms in...Ch. 14.5 - Prob. 2AYUCh. 14.5 - Prob. 3AYUCh. 14.5 - Prob. 4AYUCh. 14.5 - In Problems 5 and 6, refer to the illustration....Ch. 14.5 - Prob. 6AYUCh. 14.5 - Prob. 7AYUCh. 14.5 - Prob. 8AYUCh. 14.5 - Prob. 9AYUCh. 14.5 - Prob. 10AYUCh. 14.5 - Prob. 11AYUCh. 14.5 - Prob. 12AYUCh. 14.5 - Prob. 13AYUCh. 14.5 - Prob. 14AYUCh. 14.5 - Prob. 15AYUCh. 14.5 - Prob. 16AYUCh. 14.5 - Prob. 17AYUCh. 14.5 - Prob. 18AYUCh. 14.5 - Prob. 19AYUCh. 14.5 - Prob. 20AYUCh. 14.5 - Prob. 21AYUCh. 14.5 - Prob. 22AYUCh. 14.5 - Prob. 23AYUCh. 14.5 - Prob. 24AYUCh. 14.5 - In Problems 23-30, an integral is given. (a) What...Ch. 14.5 - Prob. 26AYUCh. 14.5 - Prob. 27AYUCh. 14.5 - Prob. 28AYUCh. 14.5 - Prob. 29AYUCh. 14.5 - Prob. 30AYUCh. 14.5 - Prob. 31AYUCh. 14.5 - Prob. 32AYUCh. 14 - Prob. 1RECh. 14 - Prob. 2RECh. 14 - Prob. 3RECh. 14 - Prob. 4RECh. 14 - Prob. 5RECh. 14 - Prob. 6RECh. 14 - Prob. 7RECh. 14 - Prob. 8RECh. 14 - Prob. 9RECh. 14 - Prob. 10RECh. 14 - Prob. 11RECh. 14 - Prob. 12RECh. 14 - Prob. 13RECh. 14 - Prob. 14RECh. 14 - Prob. 15RECh. 14 - Prob. 16RECh. 14 - Prob. 17RECh. 14 - Prob. 18RECh. 14 - Prob. 19RECh. 14 - Prob. 20RECh. 14 - Prob. 21RECh. 14 - Prob. 22RECh. 14 - Prob. 23RECh. 14 - Prob. 24RECh. 14 - Prob. 25RECh. 14 - Prob. 26RECh. 14 - Prob. 27RECh. 14 - Prob. 28RECh. 14 - Prob. 29RECh. 14 - Prob. 30RECh. 14 - Prob. 31RECh. 14 - Prob. 32RECh. 14 - Prob. 33RECh. 14 - Prob. 34RECh. 14 - Prob. 35RECh. 14 - Prob. 36RECh. 14 - Prob. 37RECh. 14 - Prob. 38RECh. 14 - Prob. 39RECh. 14 - Prob. 40RECh. 14 - Prob. 41RECh. 14 - Prob. 42RECh. 14 - Prob. 43RECh. 14 - Prob. 44RECh. 14 - Prob. 45RECh. 14 - Prob. 46RECh. 14 - Prob. 47RECh. 14 - Prob. 48RECh. 14 - Prob. 49RECh. 14 - Prob. 50RECh. 14 - Prob. 51RECh. 14 - Prob. 52RECh. 14 - Prob. 53RECh. 14 - Prob. 54RECh. 14 - Prob. 55RECh. 14 - Prob. 56RECh. 14 - Prob. 57RECh. 14 - Prob. 58RECh. 14 - Prob. 59RECh. 14 - Prob. 60RECh. 14 - Prob. 61RECh. 14 - Prob. 62RECh. 14 - Prob. 63RECh. 14 - Prob. 64RECh. 14 - Prob. 65RECh. 14 - Prob. 66RECh. 14 - Prob. 67RECh. 14 - Prob. 68RECh. 14 - Prob. 69RECh. 14 - Prob. 70RECh. 14 - Prob. 71RECh. 14 - Prob. 72RECh. 14 - Prob. 73RECh. 14 - Prob. 74RECh. 14 - Prob. 75RECh. 14 - Prob. 76RECh. 14 - Prob. 77RECh. 14 - Prob. 78RECh. 14 - Prob. 79RECh. 14 - Prob. 80RECh. 14 - Prob. 81RECh. 14 - Prob. 82RECh. 14 - Prob. 83RECh. 14 - Prob. 84RECh. 14 - Prob. 1CTCh. 14 - Prob. 2CTCh. 14 - Prob. 3CTCh. 14 - Prob. 4CTCh. 14 - Prob. 5CTCh. 14 - Prob. 6CTCh. 14 - Prob. 7CTCh. 14 - Prob. 8CTCh. 14 - Prob. 9CTCh. 14 - Prob. 10CTCh. 14 - Prob. 11CTCh. 14 - Prob. 12CTCh. 14 - Prob. 13CTCh. 14 - Prob. 14CTCh. 14 - Prob. 15CTCh. 14 - Prob. 16CTCh. 14 - An object is moving along a straight line...

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