Suppose $f(x,y) = 4-x^{2}-y^{2}$ and $R$ is the rectangle with vertices (0,0), (6,0), (6,4), (0,4). In each part, estimate $\displaystyle \iint\limits_R f(x,y) \, dA$ using Riemann sums. For underestimates or overestimates, consistently use either the lower left-hand corner or the upper right-hand corner of each rectangle in a subdivision, as appropriate.

(a) Without subdividing $R$,
Underestimate =
Overestimate =

(b) By partitioning $R$ into four equal-sized rectangles.
Underestimate =
Overestimate =