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Chapter 14: Q. 33 (page 883)

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

limx鈫�1x3-1x-1.

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)=x3-1x-1

Put x=1in the numerator we get,

x3-1=13-1=1-1=0.

Put x=1in the denominator we get,

x-1=1-1=0.

Since both numerator and denominator gives 0 means they both have x=1as their common root.

02

Step. 2 Factorizing 

Denominator has only one factor i.e., x-1.

Numerator , x3-13=(x-1)(x2+x+1).

So,

limx鈫�1x3-1x-1=limx鈫�1(x-1)(x2+x+1)(x-1)=limx鈫�1x2+x+1

Now we can put the limit directly.

03

Step. 3 Final calculation of the limit 

limx鈫�1x2+x+1=12+1+1=3.

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