Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
Callisto
Group Title
Find the limit:\[\lim_{x \rightarrow \infty} (\frac{x+2}{x1})^x\]
 one year ago
 one year ago
Callisto Group Title
Find the limit:\[\lim_{x \rightarrow \infty} (\frac{x+2}{x1})^x\]
 one year ago
 one year ago

This Question is Closed

Callisto Group TitleBest ResponseYou've already chosen the best response.0
Let \(y= (\frac{x+2}{x1})^x\) \[ln y = x\ln(\frac{x+2}{x1})\]Can't use L'Hopital's Rule now..Hmm..
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.2
I was thinking something like this: \( \displaystyle \frac{x + 2}{x  1} = \frac{x  1 + 3}{x  1} = \frac{x  1}{x  1} + \frac{3}{x  1} = 1 + \frac{3}{x1}\) The end expression looks a lot more like the definition of e in terms of limits (lim as x appraoches infinity of (1 + 1/x)^x
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.2
You CAN apply L'Hop Rule Callisto, we just need to apply a tiny trick from the spot you got to. You want to write the x as the reciprocal of the reciprocal of x.\[\huge x\ln\left(\frac{x+2}{x1}\right)=\frac{\ln\left(\frac{x+2}{x1}\right)}{\frac{1}{x}}\] And you'll notice that from here, we get an indeterminate form, 0/0 which allows us to apply L'Hop.
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.0
@zepdrix My bad, I should have revised more... Thanks a ton!!! @AccessDenied I haven't thought of this way... :'( Perhaps I should give a try!!
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.2
Definition of e? :) Hmm that's clever, yah I like that.
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.2
Yea, I vaguely recall seeing it done somewhere, it seemed like it would be pretty useful here. :P
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.2
I remember it comes up if you need to use the Limit Definition of a Derivative to show the derivative of ln x. That one is kinda fun :3
 one year 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.