Question

What is the limit as x approaches +infinity of x^100/e^x? Use L'Hopital?

Answer 1

derive the top; derive the bottom; and apply the value of x=inf

Answer 2

I did that, but in doing the derivatives, I got 100x^99/e^x, which when evaluated at infinity is still infinity over infinity, which gets me no where....if I'm doing that right?

Answer 3

http://www.wolframalpha.com/input/?i=limit+%7Bx+to+infinity%7D++x%5E100%2Fe%5Ex
this is to verify the answer

Answer 4

0

Answer 5

with your eyeballs

Answer 6

1/e^x = e^(-x) right?

Answer 7

http://www.wolframalpha.com/input/?i=100000000000%2Fe%5Ex

Answer 8

point is that you can use l'hopitals rule if you like. you will use it 100 times. the degree of the numerator will decrease by 1 each time and the denominator will still be

\[e^x\]

Answer 9

the real point is that in the long run
\[e^x\] grows faster than any polynomial, no matter what the degree. that is why i said you do it with your eyeballs

Answer 10

ah..I got it now. Thanks guys.

Answer 11

so no, you do not need l'hopital. just know that exponentials grow faster than polynomials

Answer 12

yw

Answer 13

it helps to know the limit of e^(-x) as x gets larger :)

Answer 14

oh look i didn't even notice until now! i am a
\[\color{green}{\text{guru}}\]

Answer 15

How about x! ?

Answer 16

lol .... guess you made it to 70; im wondering what the 80s are gonna be ::hoping megamind:: lol

Answer 17

that is a good question. but of course x! is not a polynomial!

Answer 18

the 80's will feature new wave music and good drugs

Answer 19

the editor will need to be upgraded for that...

Answer 20

ho ho. btw i n! grows faster than exp(n) yes?

Answer 21

Yes, I reckon..

Answer 22

While I am in here, is the javascript on the site causing headaches for anyone?

I'm having to use Safari, the others keep crashing.