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Question

Let f:RR be such that f(1) =2, f'(1)= 4 then the limx0[f(1+x+x2)+xf(1+x)f(1)]1x(x+1) = _______

A
e
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B
e12
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C
e2
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D
e3
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Solution

The correct option is A e

Since indetermined form is 1

So,

limx0[f(1+x+x2)+xf(1+x)1f(1)]1x(x+1)=limx0e1x(x+1)f(1+x+x2)+xf(1+x)1f(1)=limx0e1x(x+1)xf(1+x)f(1)=e1=e


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