JEE MATHEMATICS MCQ: LIMITS

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Analyzing +4 | -1

f(x+y)=f(x)+f(y)

for all

x, y \in R

and

f(1)=1

, then

\lim \limits_{{x \rightarrow 0}} \frac{2^{f(\tan x)}-2^{f(\sin x)}}{x^2 f(\sin x)}

equals

View answer and explanation

Correct option: C

\log \sqrt{2}

Option C (

\log \sqrt{2}

) is correct because after simplifying the expression using the given functional equation and limit properties, the limit evaluates to

\frac{1}{2} \log 2 = \log \sqrt{2}

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