Using Limit Laws to find f(x)

  1. 1. The problem statement, all variables and given/known data
    lim ( f(x)/(x2) )= 8
    x→0

    Then what is...

    a)lim ( f(x) )
    x→0

    b)lim ( f(x)/x )
    x→0




    2. Relevant equations



    3. The attempt at a solution

    tried separating the limits
    (lim x→0 f(x))(lim x→0 1/(x2)) = 8

    but the lim x→0 1/(x2) is ∞ ... soooo i dont know...
     
    Last edited: Feb 1, 2012
  2. jcsd
  3. tiny-tim

    tiny-tim 26,054
    Science Advisor
    Homework Helper

    welcome to pf!

    hi jmm12! welcome to pf! :wink:

    tell us what you think (and why), and then we'll comment! :smile:
     
  4. Re: welcome to pf!

    its in my post now, please help
     
  5. HallsofIvy

    HallsofIvy 40,310
    Staff Emeritus
    Science Advisor

    The only thing in your post is
    and that is NOT in general true. Since the denominator goes to 0, what must the numerator go to in order that this limit exist?
     
  6. tiny-tim

    tiny-tim 26,054
    Science Advisor
    Homework Helper

    draw the graph of 1/x2 (near zero) …

    roughly what do you think the graph of f(x) will have to look like if f(x)/x2 -> 8 ? :wink:
     
  7. so if the numerator has to be zero too..
    then the lim x->0 f(x) is zero??????????
     
  8. tiny-tim

    tiny-tim 26,054
    Science Advisor
    Homework Helper

    that's correct! :smile:

    but now prove it ! :biggrin:
     
  9. what would lim f(x) / x as x->0 be then..

    if (lim x->0 f(x)) / (lim x->0 x)

    0/0...or dne?
     
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