Evaluate
$$\lim_{x \rightarrow \frac{ \pi^- }{ 2 }}e ^{tanx}$$

Question

Evaluate
$$\lim_{x \rightarrow \frac{ \pi^- }{ 2 }}e ^{tanx}$$

anonymous · Answer

I don't understand why the answer is positive infinity.

misty1212 · Answer

$$\huge \lim_{x \rightarrow \frac{ \pi}{ 2 }^-}e ^{\tan(x)}$$

rational · Answer

$e^x$ is a continuous function,  so 
$$\lim (e^{f(x)}) = e^{\lim (f(x))}$$

misty1212 · Answer

just trying to read it is all

misty1212 · Answer

goes to $\frac{\pi}{2}$ from the left

misty1212 · Answer

|dw:1432605794160:dw|

misty1212 · Answer

tangent is going to $+\infty$

anonymous · Answer

what @misty1212  said
tangent goes to plus infinity so $e^{\tan(x)}$ goes to infinity real real real fast

anonymous · Answer

Oh okay. Just wondering can I sub in the pi/2 into the tanx? Does that help me?

anonymous · Answer

no

anonymous · Answer

since $\frac{\pi}{2}$ is not in the domain of tangent you cannot do that

anonymous · Answer

otherwise that would be the right thing to do, but not in this case

anonymous · Answer

So the only way to solve this is to think logically?

anonymous · Answer

heaven forbid

anonymous · Answer

i mean "yes"

rational · Answer

|dw:1432606236453:dw|

anonymous · Answer

oh, pi/2 is vertical asymptote

rational · Answer

its much worse than that, 
as you walk from left side it goes to +infinity
as you walk from right side it goes to -infinity

rational · Answer

so sometimes we say the two sided limit for  $\tan x$ as $x\to \pi/2$ does not exist

anonymous · Answer

Okay, thank you!