JEE Mains · Maths · STD 11 - 12. limits
If \(\alpha\) is the positive root of the equation, \(p(x)=x^{2}-x-2=0,\) then \(\lim \limits_{x \rightarrow \alpha^{+}} \frac{\sqrt{1-\cos (p(x))}}{x+\alpha-4}\) is equal to
- A \(\frac{3}{\sqrt{2}}\)
- B \(\frac{3}{2}\)
- C \(\frac{1}{\sqrt{2}}\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{3}{\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
\(x^{2}-x-2=0\) roots are \(2 -1\) \(\Rightarrow \lim _{x \rightarrow 2^{+}} \frac{\sqrt{1-\cos \left(x^{2}-x-2\right)}}{(x-2)}\) \(=\lim _{x \rightarrow 2^{+}} \frac{\sqrt{2 \sin ^{2} \frac{\left(x^{2}-x-2\right)}{2}}}{(x-2)}\)…
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