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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 → 0 xcot(4x) tan^ 2 (3x)cot^ 2 (6x) is equal to

The value of \lim_{x \to 0}\dfrac{xcot\left(4x\right)}{tan^{2}\left(3x\right)cot^{2}\left(6x\right)} is equal to

Options

  1. A00
  2. B44
  3. C29\dfrac{2}{9}
  4. D11

Correct answer

D. 11

Step-by-step solution

lim⁡x→09x2(tan⁡3x)219x⋅(tan⁡6x)236⋅x2⋅4x(tan⁡4x)36x24x\lim_{x \to 0}\dfrac{9x^{2}}{{\left(\tan 3x\right)}^{2}}\dfrac{1}{9x} ⋅ \dfrac{{\left(\tan 6x\right)}^{2}}{36 ⋅ x^{2}} ⋅ \dfrac{4x}{\left(\tan 4x\right)}\dfrac{36x^{2}}{4x}
=1×19×1×1×364=1= 1 \times \dfrac{1}{9} \times 1 \times 1 \times \dfrac{36}{4} = 1
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