Expert: Paul Klarreich - 2/15/2011

Question
[Question]
lim f(x) =1- e^(1/2- 1/x) as x approaches infinity


[Difficulty]
lim 1 - lim e^(1/2 - 1/x) as x approaches infinity.
1- lim e^1/2/ lim e^1/x
1- e^1/2 / (lim e^1/x)

I am stuck here. I don't know how can I find the limit of e^1/x
without knowing it beforehand.

Answer
Questioner: Sandy
Country: United States
Category: Calculus
Private: No
Subject: AP calculus ab
Question: [Question]
lim f(x) = 1- e^(1/2- 1/x) as x approaches infinity


[Difficulty]
lim 1 - lim e^(1/2 - 1/x) as x approaches infinity.
1- lim e^1/2/ lim e^1/x
1- e^1/2 / (lim e^1/x)

I am stuck here. I don't know how can I find the limit of e^1/x
without knowing it beforehand.
..................................


1- lim e^1/2/ lim e^1/x

As  x --> inf, 1/x --> 0, so e^(1/x) --> e^0 = 1.

That does not seem difficult; maybe you entered it wrong.
Take another look.