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Chapter 14: Q. 35 (page 883)

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

limx鈫�-1x+12x2-1.

Short Answer

Expert verified

The answer is 0.

Step by step solution

01

Step. 1 Given Information

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

f(x)=x+12x2-1

Put x=-1in the numerator we get,

x+12=-1+12=0.

Put x=-1in the denominator we get,

x2-1=-12-1=1-1=0.

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

02

Step. 2 Factorizing 

Denominator,x2-1=(x+1)(x-1).

Numerator ,x+12=(x+1)(x+1).

So,

limx鈫�-1(x+1)2x2-1=limx鈫�-1(x+1)(x+1)(x+1)(x-1)=limx鈫�-1x+1x-1.

Now we can put the limit directly.

03

Step. 3 Final calculation of the limit 

limx鈫�-1x+1x-1=-1+1-1-1=0-2=0.

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