Posted by ELIZABETH on Thursday, May 31, 2012 at 2:01pm.
What is the limit of the following equation?
Limit as x approaches infinity of ((e^x)  ln(x)) / (x^3)

Calculus  MathMate, Thursday, May 31, 2012 at 3:54pm
Since both numerator and denominator approach infinity as x→∞, we can apply l'HÃ´pital'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 ∞.