Use the function nest to evaluate p(x) = 1 + x + · · · + x50 at x = 1.00001. (use the matlab ones command to save typing.) find the error of the computation by comparing with the equivalent expression q(x) = (x51 − 1)/(x − 1).
The volume of a spherical hot air balloon v(r) = 4 3 ? r3 changes as its radius changes. the radius is a function of time given by r(t) = 3t. find the instantaneous rate of change of the volume with respect to t at t = 2.