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\[\lim_{x \rightarrow a}\frac{ x^{4}-a^{4} }{ x-a }\]
Wolfram says it = 4a^3 I can't see how. :\

this is the derivative of the function\[f(x)=x^4\] at x=a don you see why

So just power rule it to be 4a^3, skipping any other steps?

using \[\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}\]

That's assuming you've already taken up derivatives...

\[=f'(x)\]

Treat \[x ^{4}-a ^{4}\] as \[(x ^{2})^{2}-(a ^{2})^{2}\]
then it's algebra.

No need for a derivative. Factor the numerator.

i was just giving for a general \[\frac{x^n-a^n}{x-a}\]

I did do 4(x-a)/(x-a) but then that just leaves 4 if x-a and x-a cancel one another.

Yeah... but
\[\large \frac{4(x-a)}{x-a}\ne\frac{x^4-a^4}{x-a}\]

4 there is an exponent, not a factor ;)

Ahh yeah, I don't know why I was thinking that lol.

|dw:1364049326451:dw|
From here it's simple algebra...

binomial theorem ie

hey that was good y did you delete

I'll remember that @terenzreignz :)