TS EAMCET · Maths · Limits
\(\lim _{x \rightarrow \pi / 6}\left[\frac{3 \sin x-\sqrt{3} \cos x}{6 x-\pi}\right]\) is equal to :
- A \(\sqrt{3}\)
- B \(\frac{1}{\sqrt{3}}\)
- C \(\frac{1}{\sqrt{3}}\)
- D \(-\frac{1}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow \frac{\pi}{6}} \frac{3 \sin x-\sqrt{3} \cos x}{6 x-\pi}\) Using L, Hospitals' rule, \(=\lim _{x \rightarrow \frac{\pi}{6}} \frac{3 \cos x+\sqrt{3} \sin x}{6}\)…
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