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Question

If f(1)=1,f'(1)=2, then limx1[f(x)-1]/(x-1)=


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Solution

Finding the value of limx1[f(x)-1]/(x-1):

Given that f(1)=1,f'(1)=2

limx1[f(x)-1]/(x-1)

Applying L.Hospital rule (00form)

limx112f(x)f'(x)-012x-0=limx1f'(x)f(x)1x=limx1f'(x)1f(1)=2×1/1=2

Hence, the value of limx1[f(x)-1]/(x-1)=2


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