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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Limits

NDA 2013 · Mathematics · Limits

What is _ x arrow 0 ( 2 x+4 x)/(2 x+ 4 x) equal to?

What is lim⁡x→0sin⁡2x+4x2x+sin⁡4x\lim _{x \rightarrow 0} \frac{\sin 2 x+4 x}{2 x+\sin 4 x} equal to?

Options

  1. A0
  2. B12\frac{1}{2}
  3. C1
  4. D2

Correct answer

C. 1

Step-by-step solution

lim⁡x→0sin⁡2x+4x2x+sin⁡4x=lim⁡x→02⋅sin⁡2x2x+4xx2xx+4⋅sin⁡4x4x=2+42+4=66=1\begin{aligned} & \lim _{x \rightarrow 0} \frac{\sin 2 x+4 x}{2 x+\sin 4 x} \\ & =\lim _{x \rightarrow 0} \frac{\frac{2 \cdot \sin 2 x}{2 x}+\frac{4 x}{x}}{\frac{2 x}{x}+\frac{4 \cdot \sin 4 x}{4 x}} \\ & =\frac{2+4}{2+4}=\frac{6}{6}=1\end{aligned}
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