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Chapter 14: Q. 36 (page 883)

In Problems 7鈥� 42, find each limit algebraically.

limx鈫�2x3-8x2-4.

Short Answer

Expert verified

The answer is 3.

Step by step solution

01

Step. 1 Given Information

Firstly, we check whether the given function is in indeterminant form or not.

f(x)=x3-8x2-4

Put x=2in the numerator we get,

x3-8=23-8=8-8=0.

Put x=2in the denominator we get,

x2-4=22-4=4-4=0.

Since both numerator and denominator gives 0 means they both have x=2as their common root.

02

Step. 2 Factorizing 

Denominator,x2-4=(x+2)(x-2).

Numerator ,x3-8=(x-2)(x2+2x+4).

So,

limx鈫�2x3-8x2-4=limx鈫�2(x-2)(x2+2x+4)(x-2)(x+2)=limx鈫�2x2+2x+4x+2.

Now we can put the limit directly.

03

Step. 3 Final calculation of the limit  

limx鈫�2x2+2x+4x+2=4+4+42+2=124=3.

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Most popular questions from this chapter

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