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Confused on problem, as p approaches a

  1. Sep 22, 2005 #1
    Hello everyone, i'm alittle confused on this problem...
    Suppose that f(x) = x^3 for all numbers x. If a is a number, determine what
    [f(p) - f(a)]/p-a approaches as p approaches a.
    I plugged in the f(x) and got:
    [p^3-a^3]/(p-a) = [(p-a)(p^2 + ax +a^2)]/p-a = p^2+ax+a^2

    I ended up figuring out a similar problem:
    f(x) = x^2 determine what [f(p) - f(a)]/p-a approaches as p approaches a. and I got an answer of 2a, because it simplied down to (p+a), because as p gets closer and closer to a its really almost a so you can say, (p+a) as p approaches a is 2a, which was right. Any help would be great!
     
  2. jcsd
  3. Sep 22, 2005 #2
    look at your expansion of [tex] p^3 - a^3 [/tex]
    what is it SUPPOSED to be
    [tex] (p-a)(p^2+ap+a^2) [/tex]
    instead of your ax term

    and as p approaches a you get
    [tex] a^2 + a^2 + a^2 = 3a^2[/tex]
     
  4. Sep 22, 2005 #3
    ohhh!! thanks so much, i don['t see why i didn't catch that!
     
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