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: Pointwise convergence of (x^n)/(1 + x^n)

  1. Dec 1, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the function that (x^n)/(1 + x^n) converges to as n goes to infinity, on the interval [0,2]

    2. Relevant equations

    3. The attempt at a solution
    I've worked out the fact that on the interval [0,1) it converges to 0, and when x is 1 it converges to 1/2, but for the life of me I'm not sure what the first step of proving what it converges to on the (1,2] interval. hints?
  2. jcsd
  3. Dec 1, 2011 #2


    User Avatar
    Science Advisor
    Homework Helper

    Divide numerator and denominator by x^n. Now can you figure out what it converges to on (1,2]?
  4. Dec 1, 2011 #3
    Yes! It becomes 1 / ( 1/(x^n) + 1), which goes to 1 / (0+1) = 1.

    Thank you so much :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook