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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!