1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Limit of a Sequence

  1. Apr 16, 2010 #1
    1. The problem statement, all variables and given/known data

    Show convergence or divergence, find the limit of the sequence.

    2. Relevant equations




    3. The attempt at a solution

    See the attached picture. Sorry, it was taking way longer to figure out how to input the TeX than it was to just snap and crop a picture of my work.

    My question is: where did I lose the coefficient 4? The correct answer is supposed to be convergent, a_n --> infinity = 4

    Attached Files:

  2. jcsd
  3. Apr 16, 2010 #2
    In the step
    [tex]\lim_{x\rightarrow\infty} y = 4\lim_{x\rightarrow\infty}x^{\frac{1}{x}} \Leftrightarrow \lim_{x\rightarrow\infty}\ln y = 4\lim_{x\rightarrow\infty}\ln x^{\frac{1}{x}}[/tex]
    you forgot to take the logarithm of the 4 on the right hand side.
  4. Apr 16, 2010 #3
    True, but how does that affect the outcome? The limit(x-->infinity) of 1/x = 0 thus negating anything else that multiplies against it, which still leads me back to e^0 = 1.

    NvM, I see that I need to put the 4 back inside the limit then with log properties it becomes ln4+ln(1/x)... e^ln4 = 4... therefore a_n-->4. It's not always obvious to me when I should factor constants out or just leave them be.

    Thanks for pointing that out, NeoDevin!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook