Confused on problem, as p approaches a

  • Thread starter mr_coffee
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  • #1
mr_coffee
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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!
 

Answers and Replies

  • #2
stunner5000pt
1,455
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]
 
  • #3
mr_coffee
1,629
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ohhh! thanks so much, i don['t see why i didn't catch that!
 

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