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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Limits

NTA Abhyas 2020 · Mathematics · Limits

The value of _ x → π (π ^ 2 x ) ^ 2 x is equal to

The value of lim⁡x→πtan⁡(πcos⁡2x)sin⁡2x\lim_{x \to \pi}\dfrac{\tan (\pi\cos^{2} x )}{\sin^{2} x} is equal to

Options

  1. A11
  2. Bπ\pi
  3. C−π- \pi
  4. Dπ2\dfrac{\pi}{2}

Correct answer

C. −π- \pi

Step-by-step solution

Let, x=π+tx = \pi + t

\lim_{t \to 0} \dfrac{\text\tan\left(\pi\cos^{2} ( \pi + t )\right)}{\sin^{2} ( \pi + t )} ⇒ \lim_{t \to 0} \dfrac{\tan ( \pi\cos^{2} t )}{\sin^{2} t}

lim⁡t→0tan⁡(π−πsin⁡2t)sin⁡2t⇒lim⁡t→0−tan⁡(πsin⁡2t)πsin⁡2t⋅π=−π\lim_{t \to 0} \dfrac{\tan \left(\pi - \pi\sin^{2} t\right)}{\sin^{2} t} ⇒ \lim_{t \to 0} \dfrac{- \tan ( \pi\sin^{2} t )}{\pi\sin^{2} t} \cdot \pi = - \pi
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