JEE MATHEMATICS MCQ: LIMITS

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Application +4 | -1

\lim \limits_{{x \rightarrow 0}}\left(\frac{\ln (a+x)-\ln a}{x}\right)+k \lim \limits_{{x \rightarrow e}} \frac{\ln x-1}{x-e}=1

then

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Correct option: A

k=e\left(1-\frac{1}{a}\right)

Option A (

k=e\left(1-\frac{{1}}{{a}}\right)

) is correct because by applying the definition of derivative and simplifying, we can find the value of k.

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