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Chapter 14: Q. 45 (page 889)

In Problems 45-60, determine whether fis continuous at c.

f(x)=x3-3x2+2x-6,c=2

Short Answer

Expert verified

The function is continuous atc

Step by step solution

01

Given information

Given function

f(x)=x3-3x2+2x-6c=2

02

Check whether the function is defined at c

Checking, we get

f(2)=23-3(2)2+2(2)-6f(2)=8-3(4)+2(2)-6f(2)=8-12+4-6f(2)=-6

So it is defined atc

03

Check the left hand limits and right hand limits

We have,

limx鈫�2-f(x)=23-3(2)2+2(2)-6limx鈫�2-f(x)=8-3(4)+2(2)-6=-6

Again,

limx鈫�2+f(x)=limx鈫�2+23-3(2)2+2(2)-6limx鈫�2+f(x)=limx鈫�2+8-3(4)+2(2)-6limx鈫�2+f(x)=-6

Since limx鈫�cf(x)=f(c)so it is continuous atc

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