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Also need help with Limits!

  1. Mar 22, 2008 #1
    1. The problem statement, all variables and given/known data
    A) lim as x-1 of x^2-x+1/x+1 =1/2

    B)lim as x-0 of x^2 sin(1/x)=0

    C) lim as x-1+ of 2^1/x-1=infinity

    2. Relevant equations
    By delta-epsilon proofs

    3. The attempt at a solution

    A) I took |f(x)-l| and could not factor out an x-1

    B) I know that x^2 goes to 0 and that the compositions of functions have the same limit.

    C) I have no clue how to evaluate limits from the right hand side!
  2. jcsd
  3. Mar 22, 2008 #2
    for B, |x^2sin(1/x)| = |x^2||sin(1/x)| <= ...

    what do you know about the sine function? for all u we have |sin(u)| <= ...?
  4. Mar 22, 2008 #3
    that it is bounded by 1
  5. Mar 22, 2008 #4
    right, so let e > 0, and choose d = sqrt(e), then if |x| < d, |x^2sin(1/x)| <= |x|^2*1 < d^2 = e, i'll let you do the rest, but that's the idea though
  6. Mar 22, 2008 #5
    C) looks really hard, I wish I could help you.
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