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Question

If f(x)={x+1, if x>0x1, if x0 show that lix0f(x) does not exists.

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Solution

For limx0f(x) to exist

lhl=rhl=functional value

L.H.L

limx0h(f(x))=limh0((0h)1)=1
f(x)=x1

R.H.L

limx0+hf(x)=limh0(0+h+1)=1
x+1

L.H.LR.H.L

limit doesn't exist.


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