$\lim _\limits{x \rightarrow 0} \frac{a^x-1-x \log a}{x^2}$ is

JEE MATHEMATICS MCQ: LIMITS

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\lim \limits_{{x \rightarrow 0}} \frac{a^x-1-x \log a}{x^2}

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Correct option: B

\frac{1}{2}(\log a)^2

Option B (

\frac{1}{2}(\log a)^2

) is correct because after applying L'Hôpital's rule twice, the limit evaluates to

\frac{1}{2}(\log a)^2

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