# Confused on problem, as p approaches a

1. Sep 22, 2005

### mr_coffee

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. Sep 22, 2005

### stunner5000pt

look at your expansion of $$p^3 - a^3$$
what is it SUPPOSED to be
$$(p-a)(p^2+ap+a^2)$$
$$a^2 + a^2 + a^2 = 3a^2$$