Use a taylor series to conjecture the value of:

The limit as x approaches 0 of (sin (x^3)-(x^3))/9

2. You know that for small x (so certainly for x approaching 0), we can say that sin(x) =~ x. This follows from its Taylor series, when we neglect higher order terms (since sin(x) = x - x³/3! + ...).

So, what happens when you replace sin(x) by x?