a.) Let V=x^3. Find dV and ΔV. Show that for small values of x, the difference ΔV-dV is very small in the sense that there exists ε such that ΔV-dV=εΔx, where ε->0 as Δx->0.

b.) Generalize this result by showing that if y=f(x) is a differentiable function, then Δy-dy=εΔx, where ε->0 as Δx->0.