AP EAMCET · Maths · Limits
\(\lim _{x \rightarrow 1} \frac{\sqrt{x}-1}{\left(\cos ^{-1} x\right)^2}=\)
- A \(-\frac{1}{4}\)
- B \(\frac{1}{2}\)
- C \(-\frac{1}{2}\)
- D \(\frac{1}{4}\)
Answer & Solution
Correct Answer
(A) \(-\frac{1}{4}\)
Step-by-step Solution
Detailed explanation
Let \(x=\cos \theta \Rightarrow x \rightarrow 1 \Rightarrow \theta \rightarrow 0\) \(\lim _{x \rightarrow 1} \frac{\sqrt{x}-1}{\left(\cos ^{-1} x\right)^2}=\lim _{\theta \rightarrow 0} \frac{(\sqrt{\cos \theta}-1)}{\theta^2}\)…
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