Question

how do i find the limit as x approaches infinity of ( e^x/5x^2)

Answer 1

you could use l'hopital's rule if it is not obvious

Answer 2

you know what to do for that?

Answer 3

no can you help me?

Answer 4

take the derivative top and bottom separately

Answer 5

don't use the quotient rule
you will have to do it twice

Answer 6

oh okay

Answer 7

\[\lim_{x\to \infty}\frac{e^x}{5x^2}=\lim_{x\to \infty}\frac{e^x}{10x}=\lim_{x\to \infty}\frac{e^x}{10}\]

Answer 8

okay I'm with you so far

Answer 9

you are done at that step, since that limit is \(\infty\)

Answer 10

but really it should be pretty clear that \(e^x\) grows way way way faster than \(5x^2\) making the limit infinity for sure
pick for example \(x=100\)
the denominator is pretty big, at \(50000\) but the numerator is \(e^{100}\) which is probably too large for your calculator

Answer 11

just checked with wolfram, and \(e^{100}\) has 43 zeros!

Answer 12

lol thank you!