If u(t) = (sin(4t), cos(2t), t) and v(t) = (t, cos(2t), sin(4t)), use Formula 4 of this theorem to find d dt u ( t ) . v ( t ) . 8t cos (ut ) + 2 sin(ut) - 4 cos (2t ) sin (2t) XFind the Taylor polynomial 7,(x) for the function f centered at the number a. f(x) = xe-9x a = 0 T3(x) = x - 9x2 27 -3 2 XConsider the following function. x)=1/x, a= 1r n=2, 0.65xs 1.4 (a) Approximate f by a Taylor polynomial with degree n at the number a. (b) Use Taylor's Inequality to estimate the accuracy of the approximation x) :6 Tn(x) when x lies in the given interval. (Round your answer to eight decimal places.) |R2(x)| 5 0.0001486: x Consider the following function. f(x) = x2/5, a =1, n =3, 0.8