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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Limits

NDA 2018 · Mathematics · Limits

What is _ x arrow (π)/(6) (2 ^2 x+ x-1)/(2 ^2 x-3 x+1) to?

What is lim⁡x→π62sin⁡2x+sin⁡x−12sin⁡2x−3sin⁡x+1\lim _{x \rightarrow \frac{\pi}{6}} \frac{2 \sin ^2 x+\sin x-1}{2 \sin ^2 x-3 \sin x+1} to?

Options

  1. A-1/2
  2. B-1/3
  3. C-2
  4. D-3

Correct answer

D. -3

Step-by-step solution

lim⁡x→π6(sin⁡x+1)(2sin⁡x−1)(sin⁡x−1)(2sin⁡x−1)=12+112−1=−3\lim _{x \rightarrow \frac{\pi}{6}} \frac{(\sin x+1)(2 \sin x-1)}{(\sin x-1)(2 \sin x-1)}=\frac{\frac{1}{2}+1}{\frac{1}{2}-1}=-3
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