Question

For which pair of functions f(x) and g(x) below will the limit as x goes to infinity of the quotient of f of x and g of x equals 0? f(x) = ex; g(x) = x3 f(x) = x5; g(x) = ex f(x) = x3; g(x) = ln(x) f(x) = x−2; g(x) = e−x

Answer 1

did you through them and try to evaluate the limits?

Answer 2

\[\lim_{x \rightarrow \infty}\frac{e^x}{x^3}=?\]

Answer 3

first of all you can use l'hospital here since you have infinity over infinity

Answer 4

try the second one:- x^5 / e^x - apply l'hospitals theorem several times - what do you get?

Answer 5

r u familiar with the theorem?

Answer 6

I'm familiar with l'hospital's theorem, but I'm not sure of what the limit of e^x as x approaches infinity or likewise what ln(x) would be as x approaches infinity

Answer 7

as x approaches infinity e^x approaches infinity

Answer 8

Okay, so how would e^x as x approaches infinity ever equal zero? The derivative would just keep coming out as e^x

Answer 9

applying l'hopitals to x^5 / e^x :- f'(x) of x^5 = 5x^4 and of e^x = e^x

if we keep applying this rule sveral times we will get 5 / e^x

and limit of this as x--> infinity = 0

Answer 10

5!/e^x but yeah still goes to 0 as x goes to infinity :p

Answer 11

oh yes of course derivative of 120 goes to 0

Answer 12

so it ends up as 0 / infinity

Answer 13

Okay, I see now. Thank you guys for your help.

Answer 14

yw - also limit as x approaches infinity of lnx is infinity