Question

\[\large \displaystyle lim_{x \rightarrow \infty} x^5e^{-x}\]

Answer 1

what do you expect its answer to be ?

Answer 2

I don't know. Do you expect me to know?

Answer 3

Both terms will approach infinity as x approaches infinity

Answer 4

It's usually no good practice to write lim .. = infinity. You can always write lim .. -> infinity.
Eiher way, the person reading will most likely understand

Answer 5

What if one approaches zero and other one approaches infinity? What should I do with it?

Answer 6

Like \(\large \displaystyle lim_{x \rightarrow \infty} x^5e^{-x}\)

Answer 7

Wait did the question to e^-x? That goes to 0 because exponentials defeat polynomials

Answer 8

L'Hopitals' rule.

Answer 9

The new one will approach zero