limit of e^tanx as x approaches pi/2 from the right

I took the limit of e and multiplied it by pi/2 but cant get the answer. can someone explain please

Question

limit of e^tanx as x approaches pi/2 from the right

I took the limit of e and multiplied it by pi/2 but cant get the answer. can someone explain please

misty1212 · Answer

oh no

misty1212 · Answer

HI!!

misty1212 · Answer

first compute 
$$\lim_{x\to \frac{\pi}{2}^+}\tan(x)$$

anonymous · Answer

that would be positive infitiy right

anonymous · Answer

no i don't think so

anonymous · Answer

you are approaching from the right

anonymous · Answer

negatiuve I mean sorry lol

anonymous · Answer

yeah so $e^{-\infty}$ is the form

anonymous · Answer

okay that makes sense but now could you please explain to me why we take the limit of just the power? is it for any one with an exponent?

anonymous · Answer

It's a property of continuous functions. $e^x$ is continuous for all values of $x$, which allows you to say
$$\large \lim_{x\to c}e^{f(x)}=e^{\lim\limits_{x\to c}f(x)}$$