EBK PRECALCULUS: MATHEMATICS FOR CALCUL

6th Edition

ISBN: 9781133715047

Author: Watson

Publisher: YUZU

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Question

Chapter 2.1, Problem 30E

To determine

To evaluate f(−5),f(0),f(1),f(2),f(5) valuesby usingthe piecewise function

f(x)={3x, if x<0x+1, if 0≤x≤2(x−2)2, if x>2

Expert Solution & Answer

Answer to Problem 30E

The required functions of the values are f(−5)=−15,f(0)=1,f(1)=2,f(2)=3,f(5)=9.

Explanation of Solution

Given information: consider the piecewise function f(x)={3x, if x<0x+1, if 0≤x≤2(x−2)2, if x>2

Calculation:

First find the value of f(−5)

Since the values of x=−5<0

From the above piecewise function,to be taken as

f(x)=3x

f(−5)=3(−5)f(−5)=−15

Find the values of f(0),f(1),f(2)

Since the value of x=0,x=1<2,x=2

From the above piecewise function,to be taken as

f(x)=x+1

f(0)=0+1f(0)=1f(1)=1+1f(1)=2f(2)=2+1f(2)=3

Find the value of f(5)

Since the value of x=5>2

From the above piecewise function,to be taken as

f(x)=(x−2)2

f(5)=(5−2)2f(5)=9

Thus, the required function of the values f(−5)=−15,f(0)=1,f(1)=2,f(2)=3,f(5)=9.

Chapter 2.1, Problem 29E

Chapter 2.1, Problem 31E

Chapter 2 Solutions

EBK PRECALCULUS: MATHEMATICS FOR CALCUL

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To evaluate f ( − 5 ) , f ( 0 ) , f ( 1 ) , f ( 2 ) , f ( 5 ) valuesby usingthe piecewise function f ( x ) = { 3 x , if x &lt; 0 x + 1 , if 0 ≤ x ≤ 2 ( x − 2 ) 2 , if x &gt; 2

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To evaluate f(−5),f(0),f(1),f(2),f(5) valuesby usingthe piecewise function f(x)={3x, if x<0x+1, if 0≤x≤2(x−2)2, if x>2

Answer to Problem 30E

Explanation of Solution

Chapter 2 Solutions

To evaluate f ( − 5 ) , f ( 0 ) , f ( 1 ) , f ( 2 ) , f ( 5 ) valuesby usingthe piecewise function f ( x ) = { 3 x , if x < 0 x + 1 , if 0 ≤ x ≤ 2 ( x − 2 ) 2 , if x > 2

To evaluate f(−5),f(0),f(1),f(2),f(5) valuesby usingthe piecewise function

f(x)={3x, if x<0x+1, if 0≤x≤2(x−2)2, if x>2