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Chapter 14: Q. 30 (page 883)

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

limx鈫�-1x2+xx2-1.

Short Answer

Expert verified

The answer is12.

Step by step solution

01

Step. 1 Given Information

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

f(x)=x2+xx2-1

Since if we put x=-1we get,

-12+-1-12-1=1-11-1=00.

So the limit is in 0/0 indeterminant form.

02

Step. 2 Try to find factor which make the function indeterminant.

Since we have both polynomial functions in the numerator and denominator, So let's factorize them,

x2+xx2-1=xx+1x2-12=xx+1x+1x-1.

cancelling x+1from both numerator and denominator we get,

xx-1.

Now if we put x=-1then it is not in indeterminant from. So, now we can directly put the limit in it.

03

Step. 3 Solving the limit 

limx鈫�-1xx-1=-1-1-1=-1-2=12.

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