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GATE 2019 CE (CE1) – Question 11

Engineering Mathematics · Calculus: Limits, continuity, mean value theorems, maxima and minima, Taylor series · 1 mark · Multiple choice

Which statement about the following limits is correct? Let $L_1=\lim_{x\to0}\frac{\sin4x}{\sin2x}$ and $L_2=\lim_{x\to0}\frac{\tan x}{x}$.

  1. $L_1=2,\ L_2=1$
  2. $L_1=1,\ L_2=1$
  3. $L_1=\infty,\ L_2=1$
  4. $L_1=2,\ L_2=\infty$

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Correct answer: (A) $L_1=2,\ L_2=1$

Explanation

Using $\sin(kx)/(kx)\to1$, the first limit is $4/2=2$. Also $\tan x/x\to1$. Thus **(2, 1), A**, with angles in radians.