Question

How do I solve this. Please reply fast

Answer 1

As x approach 0, let's take a look at 1/x

LHL, 1/x approach negative infinity.

RHL, 1/x approach positive infinity.

So, LHL of asked limit = (0+1)/(0-1)=-1

And RHL of asked limit = [1+e^{-1/x}]/[1-e^{-1/x}]=1

So, limit doesn't exist.