15,16 - please help solve these problems. i will rate, thank you :)

Suppose that the position of a body moving along a coordinate line at time t is given by each function below, where a, b, and k are constants. Show in both cases that the acceleration d's dt 2 - is proportional to s but that in the first case it is directed toward the origin, whereas in the second case it is directed away from the origin. a. s = a cos kt + b sin kt b. s = a cosh kt + b sinh kt a. For the first case, the given position function is s = a cos kt + b sin kt. The velocity of the body is ds dtDetermine if the following functions grow faster, slower, or at the same rate as the function e * as x -+ co. a. 15x# + 30x + 1 b. x In 9x - X C. 13+x4 6 5x d. e. e - 5x f. xe 5x g. e COS X h. 5x - 1 a. The function 15x# + 30x + 1 grows 5x as x - co because lim 2 5x x-+ 0 15x* + 30x +1