Calculus

posted by .

What is the limit of the following equation?
Limit as x approaches infinity of ((e^x) - ln(x)) / (x^3)

• Calculus -

Since both numerator and denominator approach infinity as x→∞, we can apply l'HÃ´pital's rule:
(ex-(1/x))/3x²
Rewrite as a sum:
ex/3x² -(1/x)/3x²
the second term goes to zero as x→∞.
Apply the rule again to the first term:
ex/6x;
Apply the rule one last time:
ex/6; which goes to ∞ as x→&infin.
So the limit is ∞.

Similar Questions

1. calculus

what is the answer for the integral of (1/(xln(x)) from 1 to infinity?
2. Algebraic limits

The limit as x approaches infinity. (1)/(5^x) The limit as x approaches 1. (1-x^3)/(2-sqrt(x^2-3)) Show your work thanks in advance!
3. Calculus

Could someone please help me with these questions;I was having trouble with these four questions. Evaluate each limit, if it exists, using any appropriate technique. 1.) The limit as u approaches 4; u^2-16/u^3-64 2.) The limit as x …
4. calculus

What is the limit of the function as x approaches infinity?
5. calculus

What is the limit of the function as x approaches infinity?
6. Math-Calculus

Hi, I am trying to figure out what the limit as h approaches 0 of (1-2h)^(1/h) is. I am unfamiliar with the process I am supposed to use to solve this limit. I have just been reasoning out this limit, but I keep getting the answer, …
7. Calculus

Determine the behavior of limits A. Limit as x approaches 1 of: (log x)/((x-1)^2) B. Limit as x approaches infinity of: ((x-1)^2)/(log x))
8. Calculus

Find limit as x approaches 1 5/(x-1)^2 A. 0 B. Negative infinity C. 5/4 D. Infinity If I use limit as h approaches 0 f(x+h)-f(x)/h , will I get an x in the answer?
9. Math

f(x) = cos (1/x) Find the limit as x approaches infinity and find the limit as x approaches negative infinity. Identify all horizontal asymptotes.
10. Math

f(x) = cos (1/x) Find the limit as x approaches infinity and find the limit as x approaches negative infinity. Identify all horizontal asymptotes.

More Similar Questions