Please solve the following questions

(24) Evaluate the integral : Visin ( 1 + 23/2) dx . (25) Find the equation of the normal line to the curve sin(y) + 2ry3 + 21 = 4 at the point (2, 0). (26) Let f(x) = x2e ". For what value(s) of r 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(-?"). ( sooo) mil (2) (27) Evaluate the integral: ( 5 t + 4 ) 2.7 dt need a mil (c) (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? "TT /3 (29) Evaluate the integral: - csc' xdx. (30) Find the derivative of the integral function: g(x) = VI sec 3t tan 3tdt. Leave your answer unsimplified. (31) Use Newton's Method to make the second approximation T2 to the solution of 2et = ex. Take 1 = 1. (cos ( I ) Find the derivative: dx VI - 12 at