Question

what is the limit of tan(x) as x approaches pi

Answer 1

\[\lim_{x\to\pi^-}\tan x=\infty,\lim_{x\to\pi^+}\tan x=-\infty\]

Answer 2

\[\lim_{x\to \pi+h} \tan x= \lim_{h\to 0} \tan (pi+h)= \lim_{h\to 0} \tan h= 0\]
\[\lim_{x\to \pi-h} \tan x= \lim_{h\to 0} \tan (pi-h)= \lim_{h\to 0} -\tan h= 0\]
So
\[\lim_{x\to \pi} \tan x= 0\]

Answer 3

Woops, yeah, what Ash said. Dang, \(\frac{\pi}{2}\) was what I thought I read. XD

Answer 4

tangent is continuous at
\[pi\] so
\[\lim_{x\to \pi} \tan x=\tan(\pi)= 0\]