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

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The answer is 0, though.
This is an indeterminate form, so you need to use l'Hospital 5 times. An exponential function will beat out a polynomial eventually.

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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.
Notice that the polynomial's 5th derivative is constant, but the denominator's derivative continues to increase.
Thank you, guys. I didn't do up to 5th derivative, that's why I was confused.

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