Don't Be Tricked

Calculus Level 3

Which of the following limits tend to unity? $\begin{aligned} (A) \lim_{x \to 0} \dfrac{\sin (\tan x)}{\sin x} & & (B) \lim_{x \to \frac{\pi}{2}} \dfrac{\sin (\cos x)}{\cos x} \\ (C) \lim_{x \to 0} \dfrac{\sqrt{x^2}}{x} \qquad & & \qquad (D) \lim_{x \to \frac{\pi}{2}} \left ( \dfrac{1 - \cos x}{x^2} \right ) \\ \end{aligned}$

Select one or more

B C A D

1 solution

Naren Bhandari
Sep 22, 2018

Note that for $A$ and $B$ limit exist and limit is $1$ whenever $x\to 0$ , with case $D$ has the limit $1/2$ if $x\to \pi/2$ . However, case $C$ that there exist no limit since $\sqrt{x^2} = |x|$ , if $x\to 0^{-}$ limit is $< 0$ for $x\to 0^{+}$ limit is $>0$ . Thus $A$ and $B$ are correct choice.

I think theres a misprint in both the question and your answer, in case D, x tends to 0, not π/2 for the limit to tend to unity

Parth Sankhe - 2 years, 8 months ago

Don't Be Tricked

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