Question

What is the limit of ntan(1/n) as n approaches infinity?

Answer 1

`\displaystyle \lim_(n\to \infty) n \tan (1)/(n)=\\\\ \lim_(n\to \infty) ( \tan (1)/(n))/((1)/(n))=\\\\ \lim_(x\to 0) ( \tan x)/(x)=\\\\ \lim_(x\to 0) ( (\sin x)/(\cos x))/(x)=\\\\ \lim_(x\to 0) (\sin x )/(x \cos x)=\\\\ \lim_(x\to 0) \left((\sin x)/(x)\cdot(1)/( \cos x)\right)=\\\\ 1\cdot1=\\ 1`