JEE Mains · Maths · STD 11 - 12. limits
If the function \(f(x)=\frac{\tan (\tan x)-\sin (\sin x)}{\tan x-\sin x}\) is continuous at \(\mathrm{x}=0\), then \(f(0)\) is equal to ________
- A 2
- B 4
- C 6
- D 8
Answer & Solution
Correct Answer
(A) 2
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 0} \frac{\frac{\tan (\tan x)-\tan x}{\tan ^3 x} \frac{\tan ^3 x}{x^3}+\frac{\tan x-\sin x}{x^3}+\frac{\sin x-\sin (\sin x)}{\sin ^3 x} \frac{\sin ^3 x}{x^3}}{\frac{\tan x-\sin x}{x^3}}\) \(=\frac{\frac{1}{3}+\frac{1}{2}+\frac{1}{6}}{\frac{1}{2}}=2\)
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