A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
anyone good at limits?
lim(1+2/x)^x
x(infinity)
anonymous
 5 years ago
anyone good at limits? lim(1+2/x)^x x(infinity)

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[e^{2}\]is my guess

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0any work to go with it?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0he might be right i remember that limit i think it was either as x>0 or infinity cant remember

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[e=lim_{x>\infty}(1+\frac{1}{x})^x\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0if he is right about that one then this second one should be e^(1/[3h]) i believe

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and so of course \[e^2=lim_{x>\infty}(1+\frac{2}{x})^x\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0for exactly the same reason

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so then lim 3^(x) x>+(infinity)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if you want we can work this out step by step.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0step one is take the log get \[ln(1+\frac{1}{x})^x=xln(1+\frac{1}{x})\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0let 1/u=3h as h>0 then u>infinity so we have as u>infinity then (1+1/u)^u>e^u but u=1/(3h) so the limit is e^{1/(3h)}

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wait. myininaya i think it is just e^3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0we do it the donkey way

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0take the log, take the limit using l'hopital, see that we get 3 and then conclude that it is e^3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0which one do you want to do?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0its not fair u shouldn't always win

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0fancy which one would you like worked out?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lim 3^x x> +(infinty

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0i want to see both :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[lim_{x>\infty}3^{x}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0nothing to that one. that is \[lim_{x>\infty}\frac{1}{3^x}=0\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this is the pain: (1+2/x)^x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0as x gets large 3^x gets really large. huge denominator,1 in the numerator, very close to zero

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0back to (1+2/x)^x because i gotta go

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0take the log get xln(1+2/x) take the limit as x > infinity get infinity times 0 so rewrite

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0as \[\frac{ln(1+\frac{1}{x})}{\frac{1}{x}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now we have 0/0 so use l'hopital

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i made a mistake and wrote 1 instead of 2. when you take the derivative of to bottom you get \[\frac{1}{x^2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0when you take the derivative of the top you get \[\frac{1}{1+\frac{2}{x}}\times2\frac{1}{x^2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0everything cancels leaving you with \[\frac{2}{1+\frac{1}{x^2}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then let x > infinity and get 2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and since we took the log in the first step the answer is not 2, but e^2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so many questions, so little time
Ask your own question
Sign UpFind more explanations on OpenStudy
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.