# Homework Help: Limit of e^(1/x) as x->0

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1. Jan 9, 2017

### Phys12

In this solution, in the last 3rd line, I get the first part (-e^-1 - e^-1), however, after the '-' symbol, the person writes (1/b * e^1/b - e^1/b) and takes the limit as b->0. However, shouldn't this give him (inf. * e^inf - e^inf)?

Thanks
(His answer is correct, by the way)

2. Jan 9, 2017

### haruspex

b approaches 0 from below, so 1/b tends to minus infinity. There is a small mistake: the 1 in the (1 . 0 - 0) term. Need to use the fact that x e-x tends to 0 as x tends to +infinity.

3. Jan 9, 2017

### Phys12

Ohk! I didn't notice the fact that we were approaching 0 from the left hand side. Thanks! :)

4. Jan 9, 2017

### Ray Vickson

Right: if you approach 0 from the right the function blows up: $\lim_{x \to 0+} e^{1/x} = +\infty$.