Question

Find the Limit algebraically:
(2x+5)/(x^3-1)
The limit as x approaches infinity

Answer 1

And please explain thoroughly, I need to figure out how to do this before the test (Which is tomorrow).
Thanks for the help

Answer 2

use l'Hopital's rule. when your limit is 0/0 or inf/inf:

\[\lim \frac{ f(x) }{ g(x) } = \lim \frac{ \frac{ d }{ dx }f(x) }{ \frac{ d }{ dx } g(x)}\]

not to be confused with quotient rule.

answer should be zero

Answer 3

Hmm, let me research this rule...

Answer 4

I can't seem to understand this rule properly. Can you explain it to me please?

Answer 5

if your limit ends up being 0/0 or inf/inf you can take the derivative of the numerator and denominator and it holds true.

\[\lim_{x -> \inf} \frac{ 2x + 5 }{ x^3 - 1 } = \lim_{x -> \inf}\frac{ 2 }{ 3x^2 } = 0\]

Answer 6

Woah, I have never even heard of this before! Thanks for the help!

Answer 7

glad i could help. I just noticed it says to solve "algebraically" , which i think means we can't use calculus.

otherwise you could just do:

\[\lim_{x -> \infty} \left( \frac{ 2x }{ x^3 - 1 } + \frac{ 5 }{ x^3 - 1 } \right) = \lim_{x -> \infty} \left( \frac{ 2 }{ x^2 -\frac{ 1 }{ z } } + \frac{ 5 }{ x^3 - 1 }\right)\]

both terms give zero beause of 1/inf

Answer 8

I believe my teacher just meant that we can use our calculator, he is pretty lenient on the little things :)