Please answer the following

MTH 31 209 (20) Evaluate the integral: dx. Va (21) Let y be a function of x. Find y'(x) . Leave your answers unsimplified. (a) y = arcsin(arctan(2anx)), a ER (b) y = (VI) esec * + cos et (c) y = (22) Find the derivative of f(z) = z+ 1 2 - 1. Leave your answer unsimplified. (23) A right triangle with a hypotenuse of 6 inches is rotated about one of its legs to generate a right circular cone. What is the height of the greatest possible volume of this cone? (24) Evaluate the integral: Visin(1 + 23/2) dx. (25) Find the equation of the normal line to the curve sin(y) + 2xy3 + 2x = 4 at the point (2, 0). (6) (26) Let f(x) = x2e . For what value(s) of a does f(x) have a horizontal tangent? () (a) Find the linear approximation L(x) of f(x) = cos(x - [) at a = 0. (b) Use this to approximate cos(-?) "(teco) mil (a) (27) Evaluate the integral: ( 5t + 4 ) 2 .7 dt CJeers fall (d) (28) A particle is moving in a straight horizontal line. Its position, s(t), velocity, v(t) and ac- celeration functions, a(t) for t 2 0 are: s(t) = 13 -6t2 +9t, v(t) = 3t2 - 12t+9, a(t) = 6t-12. (a) Determine when the particle is moving to the left. (b) When is the particle speeding up? 7 /3 t nodw azoo 8.0 (29) Evaluate the integral: - csco xdx. (30) Find the derivative of the integral function: g(x) = sec 3t tan 3tdt. Leave your answer unsimplified. & (b) (31) Use Newton's Method to make the second approximation 2 to the solution of 2et = ex. Take $1 = 1. (cos (I ) (32) Find the derivative: dx VI - 12 dt )