JEE MAIN - Mathematics (2025 - 7th April Evening Shift - No. 22)
If the function $f(x)=\frac{\tan (\tan x)-\sin (\sin x)}{\tan x-\sin x}$ is continuous at $x=0$, then $f(0)$ is equal to ____________.
Answer
2
Explanation
$\lim _\limits{x \rightarrow 0} \frac{\frac{\tan (\tan x)-\tan x}{\tan ^3 x} \frac{\tan ^3 x}{x^3}+\frac{\tan x-\sin x}{x^3}+\frac{\sin x-\sin (\sin x)}{\sin ^3 x} \frac{\sin ^3 x}{x^3}}{\frac{\tan x-\sin x}{x^3}}$
$=\frac{\frac{1}{3}+\frac{1}{2}+\frac{1}{6}}{\frac{1}{2}}=2$
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