Question

lim n -> infinity (2n+ 2^n) / (3n+3^n)

Answer 1

l'hopital's rule.

Answer 2

no cant use that.....

Answer 3

is the answer 2/3?

Answer 4

not sure if its 2/3 or zero?

Answer 5

i doubt that. i think it should be zero. the first terms are irrelevant since they are linear and the rest is exponential. if we simply erase the first terms you get \[(\frac{2}{3})^n\]which certainly goes to zero. of course this is not a proof.

Answer 6

The answer is 0I used Mathematica to get the answer. I dont know how to get there though

Answer 7

yes the wolfram is also showing zero but I dont know how to get there

Answer 8

hey should I use??? |a(n) - 0 | < epsilon ???

Answer 9

i still don't know why l'hopital does not apply. take the derivative once, get \[\frac{2+2^nln(2)}{3+3^nln(3)}\]

Answer 10

I know we can use it but its analysis course, so I have to find the limit without l'hopital rule

Answer 11

do it again, get
\[\frac{2^n (ln(2))^2}{3^n (ln(3))^2}\]

Answer 12

ooh sorry.

Answer 13

any ideas you have....??? but now I m sure its 0. so I m half way I think

Answer 14

i give up :(