posted by ELIZABETH .
What is the limit of the following equation?
Limit as x approaches infinity of ((e^x) - ln(x)) / (x^3)
Since both numerator and denominator approach infinity as x→∞, we can apply l'Hôpital's rule:
Rewrite as a sum:
the second term goes to zero as x→∞.
Apply the rule again to the first term:
Apply the rule one last time:
ex/6; which goes to ∞ as x→&infin.
So the limit is ∞.