Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Closed

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
\[\lim_{x \rightarrow \infty}(\frac{ 5x3 }{ 5x+7 })^{3x+1}\]
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
take the log take the limit exponentiate
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
I am allowed to use L'Hospital's rule. I am not sure how I would use it though...
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
So I get it's (infinity/infinity)^(infinity) but I am not sure how to go from there...
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Yep... I am not sure how that would help though...
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
\[(3x+1)\ln(\frac{5x3}{5x+7})\] now you \(\infty\times 0\)
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Yep... I got there.
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
rewrite as \[\frac{\ln(\frac{5x3}{5x+7})}{\frac{1}{3x+1}}\] now you have \[\frac{0}{0}\] and now you can use l'hopital
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Hmm Okay... Let's see...
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
probably easier if you write \[\frac{\ln(5x3)\ln(5x+7)}{\frac{1}{3x+1}}\]
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Okay Thanks!
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Yep. I know.
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
@satellite73 : Okay so I have: \[\lim_{x \rightarrow \infty} \frac{ \frac{ 5 }{ 5x3 }\frac{ 5 }{ 5x+7 } }{ \frac{ 2 }{ (3x+1)^2 } }\]
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
denominator is wrong
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
\[\lim_{x \rightarrow \infty} \frac{ \frac{ 5 }{ 5x3 }\frac{ 5 }{ 5x+7 } }{ \frac{ 3 }{ (3x+1)^2 } }\]
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Chain rule. Right.
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
ugly retricealgebra from here on in have fun, but you will get a rational expression so limit is same as horizontal asymptote
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
:( . Fair enough....
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
actually it is not that bad
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Yep. I think I see why.
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
\[\frac{(3x+1)^2}{3}\times \frac{50}{(5x3)(5x+7)}\] and not need to multiply out, just look at the ratio of the leading coefficients
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
i mean you have to be a bit careful but the leading coefficient of the numerator is \(9\times 50\) and the leading coefficient of the denominator is \(3\times 25\) so you the ratio is \(6\)
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
and don't forget to exponentiate at the end
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Hmm... Okay.
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
So I got 1/e^6 or e^6.
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
:) . Thanks a million :) .
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.