Question

Find lim as x approaches to positive infinity for x^5/e^5x.

Answer 1

infinity

Answer 2

The answer is 0, though.

Answer 3

This is an indeterminate form, so you need to use l'Hospital 5 times.

An exponential function will beat out a polynomial eventually.

Answer 4

Basically, the polynomial eventually will become a constant, while the exponential function will remain an exponential function. That leaves you with a constant divided by infinity... which is 0.

Answer 5

Notice that the polynomial's 5th derivative is constant, but the denominator's derivative continues to increase.

Answer 6

Thank you, guys. I didn't do up to 5th derivative, that's why I was confused.