Posted by **Cynthia** on Friday, July 29, 2011 at 10:01am.

Using L'Hôpital's rule, evaluate lim of xe^(-x) as x approaches infinity

- calculus -
**MathMate**, Saturday, July 30, 2011 at 7:09pm
X=Lim xe^(-x)

x->∞

=Lim x/e^x

x->∞

L'hôpital's rule is applicable if direct evaluation results in an indeterminate form, which is the case here.

To apply the rule, differentiate both numerator and denominator to give

X=Lim 1/e^x

x->∞

=0

## Answer this Question

## Related Questions

- calculus, limits, l'hopital - Using l'hopital's rule, find the limit as x ...
- calculus - This is a question related to L'hopital's rule. lim x -> -infinity...
- Calculus - This is a question related to L'hopital's rule. lim x -> -infinity...
- math - Evaluate using L'Hopital Rule? lim as x approaches x from left (1-x)^(3/x...
- calculus, limits, l'hopital - Using l'hopital's rule, find the limit as x ...
- Calculus - Using L'Hopital's Rule, find the limit: lim x->0+ (as x approaches...
- calculus - Evaluate: (without using Hopital's rule) d) lim (6-3x)/(((5x+6)^1/2)-...
- calculus - The limit as x approaches infinity of (e^x+x)^(1/x). I got that it ...
- calculus - if i define the function f(x)= x^3-x^2-3x-1 and h(x) = f(x)/g(x), ...
- AP Calculus - if i define the function f(x)= x^3-x^2-3x-1 and h(x) = f(x)/g(x), ...

More Related Questions