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Question

Find limx1f(x), if f(x)={x21,x1x21,x>1

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Solution

limx1f(x)=limx1x21

Let x =1 -h, where h0

=limh0(1h)21=11=0

Now, limx1+f(x)

limx1+f(x)=limx1+x21=limh0

Let x =1-h, where h0

(1+h)21=2

Since, limx1f(x)limx1+f(x)

limx1f(x) does not exist.


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