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JEE Main 202126 FebruaryMorning Shift
Exam
JEE Main
Year
2021
Date
26 February
Shift
Morning Shift
Subject
Mathematics
Chapter
Limits

JEE Main 2021 · 26 February · Morning Shift · Mathematics · Limits

The value of _ h → 0 \ 3 sin ((π)/(6) + h) - ((π)/(6) + h) 3 h( 3...

The value of lim⁡h→0\lim_{h \to 0}\left\{\dfrac{\sqrt{3}sin\left(\dfrac{\pi}{6} + h\right) - \cos \left(\dfrac{\pi}{6} + h\right)}{\sqrt{3}h\left(\sqrt{3}cosh - sinh\right)}\right\} is :

Options

  1. A43\dfrac{4}{3}
  2. B23\dfrac{2}{\sqrt{3}}
  3. C

    23\dfrac{2}{3}

  4. D34\dfrac{3}{4}

Correct answer

C.

23\dfrac{2}{3}

Step-by-step solution

L=lim⁡h→0(3(12cosh+32sinh)−(32cosh−sinh2)(3h)(3))L = \lim_{h \to 0}\left(\dfrac{\sqrt{3}\left(\dfrac{1}{2}cosh + \dfrac{\sqrt{3}}{2}sinh\right) - \left(\dfrac{\sqrt{3}}{2}cosh - \dfrac{sinh}{2}\right)}{\left(\sqrt{3}h\right)\left(\sqrt{3}\right)}\right)

L=lim⁡h→02sinh3hL = \lim_{h \to 0}\dfrac{2sinh}{3h}

⇒L=23⇒ L = \dfrac{2}{3}

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