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Question

If f'(x)=f(x),f(0)=1, thenlimx0[f(x)-1]x=


A

0

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B

1

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C

-1

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D

2

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Solution

The correct option is A

0


Explanation for the correct option:

Find the value of limx0[f(x)-1]x:

f'(x)=f(x)f(0)=1

Applying L-Hospitals rule in limx0[f(x)-1]x we get,

limx0f'(x)-01=f'(0)f'(0)=1Given

Hence, the correct option is A.


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