Locate the discontinuity of the function:
$\Large y= \frac{1}{1+e^{\frac{1}{x}}}$

I know it is x=0, but I have to show it using limits and I'm not sure how to show it. I need to practice how to do this. Please someone help me.

Question

Locate the discontinuity of the function:
$\Large y= \frac{1}{1+e^{\frac{1}{x}}}$

I know it is x=0, but I have to show it using limits and I'm not sure how to show it. I need to practice how to do this. Please someone help me.

owlet · Answer

@freckles

owlet · Answer

@Rushwr

tkhunny · Answer

Where do things blow up?

$1+e^{something}$ is never zero, so the big fraction has to trouble.
Your ONLY problem is that pesky denominator 'x' in the exponent.

Demonstrate that the one-sided limits are not the same.

Approach from the positive side of 0.  What happens.
Approach from the negative side of 0.  What happens.

alekos · Answer

you can start by graphing the function

alekos · Answer

then working out the limits as x approaches zero from either side as tkhunny has suggested

owlet · Answer

okay thanks :)