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AP EAMCET · Maths · Limits

\(\lim _{x \rightarrow 1}\left((1-x) \tan \left(\frac{\pi x}{2}\right)\right)=\)

  1. A \(\frac{1}{\pi}\)
  2. B \(\frac{3}{\pi}\)
  3. C \(\frac{4}{\pi}\)
  4. D \(\frac{2}{\pi}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{2}{\pi}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \operatorname{Lim}_{x \rightarrow 1}(1-x) \tan \left(\frac{\pi}{2} x\right) \\ & =\operatorname{Lim}_{x \rightarrow 1} \frac{1-x}{\cot \left(\frac{\pi x}{2}\right)}=\operatorname{Lim}_{x \rightarrow 1} \frac{-1}{-\frac{\pi}{2}…