Question

how do I evaluate the limit of ( 1 - 1/x)e^1/x as x approaches 0-? I have seen someone taking s = 1/x so then it becomes ( 1-s)e^s but he said that x approaches - infinity. Can anyone explain?

Answer 1

Means what it is...
Given 1/x
as x goes to 0,
1/x gets bigger and bigger, means it goes to infinity
So when x goes to 0, 1/x, or s, goes to infinity :)

Answer 2

oh wow thanks for that :)

Answer 3

No sweat :)

Answer 4

It's a substitution.
\[x = \frac{1}{s}\iff s=\frac{1}{x}, \text{ so as $x\to0^+$, $s\to\infty$}\]