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Unreadable limit problem?

  1. Feb 3, 2014 #1
    Apostol Limit Problem?

    1. The problem statement, all variables and given/known data
    I can't afford the Apostol calculus vol. 2 there's a printing mistake in my copy of Apostol and I'm not sure how to prove this, p.251

    let f(x,y)={xsin(1/y) if y doesn't equal 0
    and f=0 if y=0
    prove that the iterated limits are not equal and that the f(x,y)->0 as (x,y)->(0,0)


    2. Relevant equations



    3. The attempt at a solution

    how exactly do you prove the limit for (x,y)->0 from all possible paths, parabolic paths, x=y, polar paths?
     
    Last edited: Feb 3, 2014
  2. jcsd
  3. Feb 3, 2014 #2

    pasmith

    User Avatar
    Homework Helper

    If this is exercise 5 of section 8.5, then what you have corresponds to my text (save that it's on page 252.)

    Use
    [tex]
    |x \sin y^{-1}| \leq |x| \leq \sqrt{x^2 + y^2}
    [/tex]
     
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