Question

lim ( tan x) = ∞

x→π/2

True or false with full explanation

Answer 1

Taking into account that $\lim\limits_{x\to\frac{\pi}{2}}\sin x=\sin\frac{\pi}{2}=1$ and $\lim\limits_{x\to\frac{\pi}{2}}\cos x=\cos\frac{\pi}{2}=0,$ we conclude that $\lim\limits_{x\to\frac{\pi}{2}}\tan x=\lim\limits_{x\to\frac{\pi}{2}}\frac{\sin x}{\cos x}=|\frac{1}{0}|=\infty.$

Answer: true