Question

Locate the discontinuities of the function.
y = 2/(1 + e^(1\/x))

Answer 1

First step, find any vertical asymptotes.

1 + e^(1/x) = 0
e^(1/x) = -1
1/x = ln(-1)
Obviously since this is impossible, there are no vertical asymptotes.

Since we have a fraction in the function (1/x), and the x is in the denominator, we can conclude that f(x) does not exist at 0, since it is undefined. We still have to make sure the limit does not exist, either though. lim(x->0+)f(x) = 0, lim(x->0-)f(x) = 2. Therefore, lim(x->0)f(x) does not exist. :)

That's it!