Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

claudiag

Hi, could anyone please help me with this limit? I know the answer's e^2 but I don't understand why: It is the limit as x goes to infinity of: (1+2/x)^x

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. Xavier
    Best Response
    You've already chosen the best response.
    Medals 0

    Try x=2a

    • 2 years ago
  2. claudiag
    Best Response
    You've already chosen the best response.
    Medals 0

    What do you mean? Do you want me to try a variable change?

    • 2 years ago
  3. Xavier
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah. Also try to use the fact that lim x->inf of (1+1/x)^x = e

    • 2 years ago
  4. reynek
    Best Response
    You've already chosen the best response.
    Medals 0

    That limit is too easy

    • 2 years ago
  5. claudiag
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok thank's, I got it already.

    • 2 years ago
  6. Shelphi
    Best Response
    You've already chosen the best response.
    Medals 0

    =e^ln((1+2/x)^x); xln(1+2/x)=ln(1+2/x)/(1/x);when x goes to infinity,it is 0/0; use L'Hospital's Rule, you will get it's goes to 2; so the ans is e^2

    • 2 years ago
  7. r1bullet
    Best Response
    You've already chosen the best response.
    Medals 0

    set y= limit (1+2_x)^x ln both sides ln y= limit ln(1+2/x)^x brinf exponent down limit x ln ( 1+2/x) now try to use l hospitals this way 1/x ln (1+2/x) take the derivative whish gets you 2... so ln y=2 its equals to y=e^2

    • 2 years ago
  8. jf2011
    Best Response
    You've already chosen the best response.
    Medals 0

    we can use \[1^{\infty}\]form for this limit. your problem is of the form lim {f(x)}^g(x) Now if f(inf) =1 and g(inf)=inf, then lim {f(x)}^(g(x) is given by e ^ {lim g(x){f(x)-1}}. here f(x) =1+2/x and g(x)=x. also, f(inf)=1+2/inf =1+0 =1 and g(inf)=inf, thus we have e^{lim x.{1+2/x-1}= e^{lim x.{2/x}=e^{lim 2} as x tends to inf leading to e^2. ALSO, visit http://sun1.sjfc.edu/~wildenbe/real_analysis/limit-problem.pdf for few more ways of looking at it.

    • 2 years ago
    • Attachments:

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.