JEE MATHEMATICS MCQ: LIMITS

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Application +4 | -1

Let

f: \mathbb{R} \rightarrow \mathbb{R}

be such that

f(1)=3

and

f^{\prime}(1)=6

. Then

\lim \limits_{{x \rightarrow 0}}\left(\frac{f(1+x)}{f(1)}\right)^{1 / x}=

View answer and explanation

Correct option: A

e^2

Option A (

e^2

) is correct because by taking the natural logarithm and applying L'Hôpital's rule, the limit simplifies to

e^2

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