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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Limits

NDA 2019 · Mathematics · Limits

What is the value of _ x arrow 0 x^ ^ 3 x^ ^ ?

What is the value of lim⁡x→0sin⁡x∘tan⁡3x∘\lim _{x \rightarrow 0} \frac{\sin x^{{}^{\circ}}}{\tan 3 x^{{}^{\circ}}} ?

Options

  1. A14\frac{1}{4}
  2. B13\frac{1}{3}
  3. C12\frac{1}{2}
  4. D1

Correct answer

B. 13\frac{1}{3}

Step-by-step solution

lim⁡x→0sin⁡x∘tan⁡3x∘×3x∘x∘×13=13lim⁡x→0(sin⁡x∘x∘)⋅(3x∘tan⁡3x∘)=13\begin{aligned} & \lim _{x \rightarrow 0} \frac{\sin x^{{}^{\circ}}}{\tan 3 x^{{}^{\circ}}} \times \frac{3 x^{{}^{\circ}}}{x^{{}^{\circ}}} \times \frac{1}{3} \\ & =\frac{1}{3} \lim _{x \rightarrow 0}\left(\frac{\sin x^{{}^{\circ}}}{x^{{}^{\circ}}}\right) \cdot\left(\frac{3 x^{{}^{\circ}}}{\tan 3 x^{{}^{\circ}}}\right) \\ & =\frac{1}{3}\end{aligned}
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