AP EAMCET · Maths · Limits
If \(f(x)=\frac{\sqrt{\pi}-\sqrt{\operatorname{Cos}^{-1} x}}{\sqrt{1+x}}\) for \(x>-1\) then \(\lim _{x \rightarrow-1^{+}} f(x)=\)
- A \(\sqrt{\frac{\pi}{2}}\)
- B \(\sqrt{\frac{2}{\pi}}\)
- C \(\sqrt{2 \pi}\)
- D \(\frac{1}{\sqrt{2 \pi}}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{\sqrt{2 \pi}}\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow-1^{+}} f(x) = \lim _{x \rightarrow-1^{+}} \frac{\sqrt{\pi}-\sqrt{\operatorname{Cos}^{-1} x}}{\sqrt{1+x}}\) Apply L'Hôpital's Rule (\(\frac{0}{0}\) form):…
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