Find the Riemann sum for f(x) = x + 3x over the interval [0, 8] (see figure), where x = 0, x1 = 1, x2 = 3, x3 = 6, and x4 = 8, and where c =1, c2 = 2, c3 = 4, and c4 = 8. y 100k 80 60 40 201 6 8 -20 Find the constant a such that the function is continuous on the entire real line. 5sin x 9(x)= if x < 0 x a-9x if x 0 Find each limit, if possible. 9-5x (a) lim xx 9x3-2 (b) lim 9-5x x-x 9x-2 (c) lim 9-5x2 x-x 9x-2 = = The function s(t) describes the motion of a particle along a line, for any time t 0. s(t) = 2-3t+5 (a) Find the velocity function v(t) of the particle at any time t 0. v(t) = (b) Identify the time interval when the particle is moving in a positive direction. 0 (---) () (0,2) (c) Identify the time interval when the particle is moving in a negative direction. (--) () (0,1)