MHT CET · Maths · Limits
If \(\mathrm{f}(x)=\left(\frac{1+\tan x}{1+\sin x}\right)^{\operatorname{cosec} x}\) is continuous at \(x=0\), then \(f(0)\) is equal to
- A 0
- B 1
- C e
- D \(\frac{1}{\mathrm{e}}\)
Answer & Solution
Correct Answer
(B) 1
Step-by-step Solution
Detailed explanation
\(\begin{aligned} f(0) & =\lim _{x \rightarrow 0} f(x) \\ & =\lim _{x \rightarrow 0}\left(\frac{1+\tan x}{1+\sin x}\right)^{\operatorname{cosec} x} \\ & =\left(\frac{1+0}{1+0}\right)^1 \\ & =1\end{aligned}\)
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