JEE Mains · Maths · STD 11 - 12. limits
\(\lim \limits_{x \rightarrow \frac{\pi}{2}}(\tan ^{2} x((2 \sin ^{2} x+3 \sin x+4)^{\frac{1}{2}}\) \(-(\sin ^{2} x+6 \sin x+2)^{\frac{1}{2}}))\) is equal to
- A \(\frac{1}{12}\)
- B \(-\frac{1}{18}\)
- C \(-\frac{1}{12}\)
- D \(-\frac{1}{6}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{12}\)
Step-by-step Solution
Detailed explanation
\(\lim \limits_{x \rightarrow \frac{\pi}{2}} \tan ^{2} x\left[\sqrt{2 \sin ^{2} x+3 \sin x+4}-\sqrt{\sin ^{2} x+6 \sin x+2}\right]\) \(=\lim \limits_{x \rightarrow \frac{\pi}{2}} \frac{\tan ^{2} x\left[\sin ^{2} x-3 \sin x+2\right]}{\sqrt{9}+\sqrt{9}}\)…
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