JEE Mains · Maths · STD 11 - 12. limits
The value of \(\lim _{x \rightarrow 0}\left(\frac{x}{\sqrt[8]{1-\sin x}-\sqrt[8]{1+\sin x}}\right)\) is equal to:
- A \(-1\)
- B \(-4\)
- C \(0\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(-4\)
Step-by-step Solution
Detailed explanation
Rationalize denominator three times \(\lim _{x \rightarrow 0} \frac{x\left\{(1-\sin x)^{1 / 8}+(1+\sin x)^{1 / 8}\right\}\left\{(1-\sin x)^{1 / 4}+(1+\sin x)^{1 / 4}\right\}\left\{(1-\sin x)^{1 / 2}+(1+\sin x)^{1 / 2}\right\}}{(1-\sin x-1-\sin x)}\)…
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