Precalculus
Precalculus
9th Edition
ISBN: 9780321716835
Author: Michael Sullivan
Publisher: Addison Wesley
Question
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Chapter 14.5, Problem 11AYU
To determine

To solve: The function ƒ( x ) = 3x + 9 is defined on the interval [ 0, 3 ] ,

a. Graph ƒ .

In (b)–(e), approximate the area A under ƒ from 0 to 3 as follows:

Expert Solution
Check Mark

Answer to Problem 11AYU

a.

Precalculus, Chapter 14.5, Problem 11AYU , additional homework tip  1

Explanation of Solution

Given:

The function ƒ( x ) = 3x + 9 is defined on the interval [ 0, 3 ] .

Calculation:

ƒ( 0 ) = 3( 0 ) + 9 = 9; ƒ( 0.5 ) = 3( 0.5 ) + 9 = 7.5; ƒ( 1 ) = 3( 1 ) + 9 = 6; ƒ( 1.5 ) = 3( 1.5 ) + 9 = 4.5

ƒ( 2 ) = 3( 2 ) + 9 = 3; ƒ( 2.5 ) = 3( 2.5 ) + 9 = 1.5; ƒ( 3 ) = 3( 3 ) + 9 = 0

a. Graph ƒ( x ) = 3x + 9

Precalculus, Chapter 14.5, Problem 11AYU , additional homework tip  2

To determine

To solve: The function ƒ( x ) = 3x + 9 is defined on the interval [ 0, 3 ] ,

b. Partition [ 0, 3 ] into three subintervals of equal length and choose u as the left endpoint of each subinterval.

Expert Solution
Check Mark

Answer to Problem 11AYU

b. 18

Explanation of Solution

Given:

The function ƒ( x ) = 3x + 9 is defined on the interval [ 0, 3 ] .

Calculation:

ƒ( 0 ) = 3( 0 ) + 9 = 9; ƒ( 0.5 ) = 3( 0.5 ) + 9 = 7.5; ƒ( 1 ) = 3( 1 ) + 9 = 6; ƒ( 1.5 ) = 3( 1.5 ) + 9 = 4.5

ƒ( 2 ) = 3( 2 ) + 9 = 3; ƒ( 2.5 ) = 3( 2.5 ) + 9 = 1.5; ƒ( 3 ) = 3( 3 ) + 9 = 0

b. Partition [ 0, 3 ] into three subintervals of equal length 1 and choose u as the left endpoint of each subinterval.

The area A is approximated as

A = f( 0 )1 + f( 1 )1 + f( 2 )1

= 9( 1 ) + 6( 1 ) + 3( 1 )

= 9 + 6 + 3

= 18

To determine

To solve: The function ƒ( x ) = 3x + 9 is defined on the interval [ 0, 3 ] ,

c. Partition [ 0, 3 ] into three subintervals of equal length and choose u as the right endpoint of each subinterval.

Expert Solution
Check Mark

Answer to Problem 11AYU

c. 9

Explanation of Solution

Given:

The function ƒ( x ) = 3x + 9 is defined on the interval [ 0, 3 ] .

Calculation:

ƒ( 0 ) = 3( 0 ) + 9 = 9; ƒ( 0.5 ) = 3( 0.5 ) + 9 = 7.5; ƒ( 1 ) = 3( 1 ) + 9 = 6; ƒ( 1.5 ) = 3( 1.5 ) + 9 = 4.5

ƒ( 2 ) = 3( 2 ) + 9 = 3; ƒ( 2.5 ) = 3( 2.5 ) + 9 = 1.5; ƒ( 3 ) = 3( 3 ) + 9 = 0

c. Partition [ 0, 3 ] into three subintervals of equal length 1 and choose u as the right endpoint of each subinterval.

The area A is approximated as

A = f( 1 )1 + f( 2 )1 + f( 3 )1

= 6( 1 ) + 3( 1 ) + 0( 1 )

= 6 + 3 + 0

= 9

To determine

To solve: The function ƒ( x ) = 3x + 9 is defined on the interval [ 0, 3 ] ,

d. Partition [ 0, 3 ] into six subintervals of equal length and choose u as the left endpoint of each subinterval.

Expert Solution
Check Mark

Answer to Problem 11AYU

d. 63 4

Explanation of Solution

Given:

The function ƒ( x ) = 3x + 9 is defined on the interval [ 0, 3 ] .

Calculation:

ƒ( 0 ) = 3( 0 ) + 9 = 9; ƒ( 0.5 ) = 3( 0.5 ) + 9 = 7.5; ƒ( 1 ) = 3( 1 ) + 9 = 6; ƒ( 1.5 ) = 3( 1.5 ) + 9 = 4.5

ƒ( 2 ) = 3( 2 ) + 9 = 3; ƒ( 2.5 ) = 3( 2.5 ) + 9 = 1.5; ƒ( 3 ) = 3( 3 ) + 9 = 0

d. Partition [ 0, 3 ] into six subintervals of equal length 0.5 and choose u as the left endpoint of each subinterval.

The area A is approximated as

A = f( 0 )( 0.5 ) + f( 0.5 )( 0.5 ) + f( 1 )( 0.5 ) + f( 1.5 )( 0.5 ) + f( 2 )( 0.5 ) + f( 2.5 )( 0.5 )

= 9( 0.5 ) + ( 7.5 )( 0.5 ) + 6( 0.5 ) + ( 4.5 )( 0.5 ) + 3( 0.5 ) + ( 1.5 )( 0.5 ) 

= 4.5 + 3.75 + 3 + 2.25 + 1.5 + 0.75

= 15.75 =  63 4

To determine

To solve: The function ƒ( x ) = 3x + 9 is defined on the interval [ 0, 3 ] ,

e. Partition [ 0, 3 ] into six subintervals of equal length and choose u as the right endpoint of each subinterval.

Expert Solution
Check Mark

Answer to Problem 11AYU

e. 45 4

Explanation of Solution

Given:

The function ƒ( x ) = 3x + 9 is defined on the interval [ 0, 3 ] .

Calculation:

ƒ( 0 ) = 3( 0 ) + 9 = 9; ƒ( 0.5 ) = 3( 0.5 ) + 9 = 7.5; ƒ( 1 ) = 3( 1 ) + 9 = 6; ƒ( 1.5 ) = 3( 1.5 ) + 9 = 4.5

ƒ( 2 ) = 3( 2 ) + 9 = 3; ƒ( 2.5 ) = 3( 2.5 ) + 9 = 1.5; ƒ( 3 ) = 3( 3 ) + 9 = 0

e. Partition [ 0, 3 ] into six subintervals of equal length 0.5 and choose u as the right endpoint of each subinterval.

The area A is approximated as

A = f( 0.5 )( 0.5 ) + f( 1 )( 0.5 ) + f( 1.5 )( 0.5 ) + f( 2 )( 0.5 ) + f( 2.5 )( 0.5 ) + f( 3 )( 0.5 )

= ( 7.5 )( 0.5 ) + 6( 0.5 ) + ( 4.5 )( 0.5 ) + 3( 0.5 ) + ( 1.5 )( 0.5 ) + 0( 0.5 )

= 3.75 + 3 + 2.25 + 1.5 + 0.75 + 0

= 11.25 =  45 4

To determine

To solve: The function ƒ( x ) = 3x + 9 is defined on the interval [ 0, 3 ] ,

f. What is the actual area A ?

Expert Solution
Check Mark

Answer to Problem 11AYU

f. 27 2

Explanation of Solution

Given:

The function ƒ( x ) = 3x + 9 is defined on the interval [ 0, 3 ] .

Calculation:

ƒ( 0 ) = 3( 0 ) + 9 = 9; ƒ( 0.5 ) = 3( 0.5 ) + 9 = 7.5; ƒ( 1 ) = 3( 1 ) + 9 = 6; ƒ( 1.5 ) = 3( 1.5 ) + 9 = 4.5

ƒ( 2 ) = 3( 2 ) + 9 = 3; ƒ( 2.5 ) = 3( 2.5 ) + 9 = 1.5; ƒ( 3 ) = 3( 3 ) + 9 = 0

f. The actual area under the graph of ƒ( x ) = 3x + 9 from 0 to 3 is the area of a right triangle whose base is of length 3 and whose height is 9. The actual area A is

Therefore

A =  1 2  base × height

A =  1 2 ( 3 ) ( 9 ) =  27 2

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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