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Question

limx(1+1x)x=


A

e

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B

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C

1

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D

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Solution

The correct option is A

e


limx(1+1x)x

At x=0, the value of the given expression is 1 form.

We can re-write as

limxexloge(1+1x)

Expansion of loge(1+x)=xx22+x33.......

limxex[1x12x2+13x3.....]

=limxe[112x+13x3.....]

put x=

We have e[10....]

=e


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