Question

Find the limit as x goes to infinity of x^20/e^x ?

Answer 1

exponential grows faster than any polynomial

Answer 2

so if the denominator grow faster to the infinity
what would the limit be?

Answer 3

you might want to recall that limit as x tends to inf of (x/e^x) is zero

Answer 4

if you did L'hospitals rule this would be much easier to take care of

Answer 5

I don't understand why that is wouldn't that give your inf/inf

Answer 6

really? you would have to do it like 20 times!
easier to eyeball it

Answer 7

Ohh I get it know thank you guys so much

Answer 8

Notice that "n" applications of lopital reduces the numerator of fraction to a constant, however not much happens in the denominator

Answer 9

\[\rm \lim\limits_{x\to \infty} \frac{x^{20}}{e^x} \stackrel{\color{red}{\text{LH 20 times}}}{\color{red}{\leadsto \leadsto\leadsto\leadsto}} \lim\limits_{x\to \infty} \frac{C}{e^x} \]

Answer 10

**nothing happens to the denominator,
its no longer in indeterminate form, you can take the limit

Answer 11

exponential growth always overtakes ANY polynomial growth if you want long enough

Answer 12

*if you wait long enough

Answer 13

nice latex \[\rm \lim\limits_{x\to \infty} \frac{x^{20}}{e^x} \stackrel{\color{red}{\text{LH 20 times}}}{\color{red}{\leadsto \leadsto\leadsto\leadsto}} \lim\limits_{x\to \infty} \frac{C}{e^x}\]

Answer 14

\[\rm \lim\limits_{x\to \infty} \frac{x^{20}}{e^x} \stackrel{\color{red}{\text{LH 20 times}}}{\color{red}{\leadsto \leadsto\leadsto\leadsto}} \lim\limits_{x\to \infty} \frac{20!}{e^x}\]