Question

use algebra to evaluate the lim->h [(8-h)^3-512]/(h)

Answer 1

Try to multiply out the (x-h)^3, not that 8^2 = 512, so those should cancel out. Eventually you should be able to eliminate the h in the denominator.

Answer 2

\[\lim_{h\to0}\frac{(8-h)^3-512}{h}=\lim_{h\to0}\frac{(512-192h+24h^2-h^3)-512}{h}=\lim_{h\to0}\frac{-192h+24h^2-h^3}{h}\]

Answer 3

Sorry, got cut off. The 512's both disappear, leaving you with \(-192h+24h^2-h^3\) in the numerator.