TS EAMCET · Maths · Limits
If \(f(x)=x \tan ^{-1} x\), then \(\lim _{x \rightarrow 1} \frac{f(x)-f(1)}{x-1}\) equals to
- A \(\frac{\pi+3}{4}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{\pi+1}{4}\)
- D \(\frac{\pi+2}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi+2}{4}\)
Step-by-step Solution
Detailed explanation
Given, \(f(x)=x \tan ^{-1} x\) then Then, \(\lim _{x \rightarrow 1} \frac{f(x)-f(1)}{x-1}\left(\frac{0}{0}\right.\) form \()\) \[ =\lim _{x \rightarrow 1} \frac{f^{\prime}(x)-0}{1} \] (using L'Hospital rule)…
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