Question

lim as x approaches 2 of (x^4 -16)/(x-2)
This is the limit definition for a derivative at a point, and I must state the function and the point.
I believe that the function would be x^4, and the point would be (2,4). Is this correct? Thanks.

Answer 1

\[\lim_{x \rightarrow 2} \frac{ x ^{4}-16 }{ x-2 }\]

Answer 2

\[\lim_{x\to2}\frac{x^4-16}{x-2}=\lim_{x\to2}\frac{(x^2-4)(x^2+4)}{x-2}=\lim_{x\to2}\frac{(x-2)(x+2)(x^2+4)}{x-2}\]