JEE MATHEMATICS MCQ: LIMITS

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Application +4 | -1

Let

f

is twice differentiable on

R

such that

f(0)=1, f^{\prime}(0)=0

and

f^{\prime \prime}(0)=-1

, then for a

\in R

\lim _{x \rightarrow \infty}\left(f\left(\frac{a}{\sqrt{x}}\right)\right)^x=

View answer and explanation

Correct option: C

e^{\frac{a^2}{2}}

Option C (

e^{\frac{a^2}{2}}

) is correct because it is the limit calculated using L'Hôpital's rule and the given conditions.

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