MHB Solving Limit Problem: $x \to 0^{-}$ e^$\frac{1}{x}$

[tmt1]

$\d{x}{{0}^{-}} e ^ {\frac{1}{x}}$

I am trying to solve this limit.

Now, if we have $\lim{x}\to{0^{-}}1/x$ , doesn't it become $\infty$?

 

[MarkFL]

Are you trying to find the following limit?

$$L=\lim_{x\to0^{-}}e^{\frac{1}{x}}$$

If so, then you should note that:

$$\lim_{x\to0^{-}}\frac{1}{x}=-\infty$$

So, what does this tell you about $L$?

 

[ineedhelpnow]

hey there. (Wave)
perhaps you remember that $\lim_{{x}\to{a}}f(g(x))=f(\lim_{{x}\to{a}}g(x))$ this is the limit continuity property.

so start of with $\lim_{{x}\to{0^-}}\frac{1}{x}$ this goes to $-\infty$ (you can show intermediate steps if necessary)

what is $e^{-\infty}$? once you determine that, you have your answer

 

[tmt1]

Can't figure out how to edit my post to fix it. It's not under thread tools

 

[ineedhelpnow]

At the bottom next to "Reply with quote" it should say edit post. if not, there is a time cap to edit posts i believe so it's possible you may no longer be able to edit it.

 

[MarkFL]

There is a 2 hour limit on editing the first post of a thread (which has now expired in this thread), and all other posts have a 24 hour limit.

You can just quote your first post, and then remove the quote tags and fix what you want to fix. :D