Question

Limit help needed.

Answer 1

\[\lim_{x \rightarrow a}\frac{ x^{4}-a^{4} }{ x-a }\]

Wolfram says it = 4a^3 I can't see how. :\

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

\[=f'(x)\]

Answer 7

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

Answer 8

Although, if you wish to be a purist, you can factor out the numerator...
\[\huge \frac{x^4-a^4}{x-a}=\frac{(x-a)(x^3+ax^2+a^2x+a^3)}{x-a}\]And the rest is dandy :D

Answer 9

No need for a derivative. Factor the numerator.

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

4 there is an exponent, not a factor ;)

Answer 14

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

Answer 15

From here it's simple algebra...