Thursday

July 31, 2014

July 31, 2014

Posted by **ELIZABETH** on Thursday, May 31, 2012 at 2:01pm.

Limit as x approaches infinity of ((e^x) - ln(x)) / (x^3)

- Calculus -
**MathMate**, Thursday, May 31, 2012 at 3:54pmSince both numerator and denominator approach infinity as x→∞, we can apply l'Hôpital's rule:

(e^{x}-(1/x))/3x²

Rewrite as a sum:

e^{x}/3x² -(1/x)/3x²

the second term goes to zero as x→∞.

Apply the rule again to the first term:

e^{x}/6x;

Apply the rule one last time:

e^{x}/6; which goes to ∞ as x→&infin.

So the limit is ∞.

**Related Questions**

calculus - What is the limit of the function as x approaches infinity? 4x^4 - 4^...

calculus - what is the answer for the integral of (1/(xln(x)) from 1 to infinity...

Calculus - Could someone please help me with these questions;I was having ...

calculus - What is the limit of the function as x approaches infinity? (x^4 - 7x...

Math-Calculus - Hi, I am trying to figure out what the limit as h approaches 0 ...

Calculus - Determine the behavior of limits A. Limit as x approaches 1 of: (log...

Help with one limit - I'm asked to find the limit as n approaches infinity of...

Algebraic limits - The limit as x approaches infinity. (1)/(5^x) The limit as x ...

Calculus - Find the limit as x approaches infinity of (lnx)^(1/x). This unit is ...

Calculus - I am maybe overthinking this, but what is the lim as n-> infinity ...