number e in calculus help gotten<<thanks to all>>

[Trezza]

The lim of e^x as x goes to inf is zero right. i think so at least.

now here rises my problem.

i am doing a workshop on relative growth and ecay rates of functions.

i am given the formula

L = lim f(x)/g(x)

we say that

1) f grows faster than g as x goes to inf if L is inf
2) f grows slower than g as x goes to inf if L is 0
3) f grows the same as g as x goes to inf if L is not zero and is finite

i have to compare several functions to e^x such that they are f(x) and e^x is g(x).

is lim of e^x won't that make for all cases of f(x) the third possiblity. it would be the lim f(x) over 0 which is an improper fration.

only thing i can think of is that i am wrong about lim of e

 

[brunswickite]

my brain shuts off in the summer

 

[Yossarian]

it has been several years since I studied calc but isn't the limit of e^x as x-> infinity, infinity?

 

[Trezza]

Originally posted by: PipBoy
it has been several years since I studied calc but isn't the limit of e^x as x-> infinity, infinity?

i don't know i hate limits i went looking in my old textbooks and i couldn't find it anywhere.

 

[brunswickite]

Originally posted by: PipBoy
it has been several years since I studied calc but isn't the limit of e^x as x-> infinity, infinity?

yea its is

think about it

e^infinity is infinite

 

[Corporate Thug]

i was thinking the same but wasnt sure so i didnt want to say it and look stupid

 

[Trezza]

ok i think i was looking at the wrong graph then if it goes to inf. there are two poorly labelled one start at ~~0,+inf and ends ~~inf,0 the other one is ~~0,-inf and ends +inf,+inf

 

[Trezza]

Originally posted by: Trezza
ok i think i was looking at the wrong graph then if it goes to inf. there are two poorly labelled one start at ~~0,+inf and ends ~~inf,0 the other one is ~~0,-inf and ends +inf,+inf

forget that i just plugged it into my graping calc (should of thought of that first) and its neither of them but i got it figured out.

 

[silverpig]

The one that rises as you go left on your graph (direction of x increasing) is e^x

The one that slopes downwards as you go left is e^-x

Just to see an estimate, say e ~ 2. Now take lim e^x as x -> inf, ~ lim 2^x as x -> inf, ~ 2^2, 2^4, 2^120, 2^1000... ~ 4, 16, 1.3292279957849158729038070602803e+36, 1.07150860718626732094842504906e+301

As you can see, as x increases, e^x will be getting friggin huge.

 

[wyvrn]

e = 2.718.., so e^infinity would be infinity