Posted by **Robert** on Friday, February 16, 2007 at 11:43am.

lim (1+x)^1/x. Give an exact answer.

x->0

This reads:

The limits as x approaches zero is (1 plus x) to the 1 divided by x.

The log of each term is

(1/x) ln (1 + x) = ln (1+x)/x

Using L'Hopital's rule for the limit of

f(x)/g(x), the limit if the log is

lim f'/g' = lim [1/(1+x)]= 1

and the antilog of that is e. 2.71828...

## Answer this Question

## Related Questions

- Calculus - We are doing limits in Calculus, but now we are doing trig limits too...
- Calc. Limits - Are these correct? lim x->0 (x)/(sqrt(x^2+4) - 2) I get 4/0...
- Maths Calculus Derivatives & Limits - Using the definition of the derivative ...
- AP Calc (Limits) - I'm trying to factor this equation in order to find its limit...
- Maths (limits) - how do i evaluated these limits: lim x --> 3 ((square root ...
- Calculus-Limits - Okay, i posted this question yesterday, however, I did not ...
- math - i need some serious help with limits in pre-calc. here are a few ...
- Calc Help - Find the derivative. Express answer in radical notation with no ...
- Limits - Lim of [1/(3+x)]-(1/3)/x as x approaches 0 is?
- Calculus - Determine the behavior of limits A. Limit as x approaches 1 of: (log...

More Related Questions