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Question

Question: \[\lim_{x \rightarrow 1}(1 + x)^{1/x} =\]...

lim⁡x→1(1+x)1/x=\lim_{x \rightarrow 1}(1 + x)^{1/x} =

A

2

B

e

C

Not defined

D

None of these

Answer

2

Explanation

Solution

lim⁡x→1(1+x)1/x=\lim _ { x \rightarrow 1 } ( 1 + x ) ^ { 1 / x } = (lim⁡x→1(1+x))lim⁡x→1(1x)=2\left( \lim_{x \rightarrow 1}(1 + x) \right)^{\lim_{x \rightarrow 1}\left( \frac{1}{x} \right)} = 2