Find

1. Find

lim x^3-b^3
x->b x^6-b^6

Where b =/= 0

It's zero. When you factor it, you get 1/(x^3 + b^3), so when x -> b, 1/(x^3 + b^3) -> 1/(2b^3), and since b =/= 0, 2b^3 cannot equal zero, and therefore 1/(2b^3) -> 1/0, and by definition lim of 1/n as n -> 0 is 0, thus 1/(2b^3) -> 0.