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Chapter 14: Q. 46 (page 889)

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

role="math" localid="1647000158813" f(x)=3x2-6x+5c=-3

Short Answer

Expert verified

The function is continuous atc

Step by step solution

01

Given information

Given the functionf(x)=3x2-6x+5

02

Check whether the function is defined at c

Checking, we get

f(-3)=3(-3)2-6(-3)+5f(-3)=3(9)-6(-3)+5f(-3)=27+18+5f(-3)=50

So the function is defined

03

Check the left hand limits and right hand limits

Checking, we get

limx鈫�3-f(x)limx鈫�3-3x2+6x+5limx鈫�3-f(x)limx鈫�3-3(3)2+6(3)+5limx鈫�3-f(x)=50

limx鈫�-3+f(x)=limx鈫�-3+3x2-6x+5limx鈫�-3+f(x)=limx鈫�-3+3(-3)2-6(-3)+5limx鈫�-3+f(x)=50

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

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