Engineering Maths and Computing 3 Continuous Assessment Name Muselli Bueno Program UT 60 30 12 (1) Find d for the following functions: (a)y- In(-x" + 8x" + sinx) (b) y = ed sin(3x) + 4x (c) V = cos 3x + 2-3 e2x - x (2) A cannon ball is propelled through the air. The height of the cannon ball, s(t) as a function of the time, t, is given by the function s(t) = 36t - 3t2 where s is in metres and t in seconds. (a) What is the velocity after 9 seconds? (b) When is the ball at its highest point? (c) What is the maximum height? (d) When does the ball fall back to the ground? (e) Sketch the graph of s(t) by using the information calculated above. (3) The MacLaurin series for a function f(x) is given by f(2) = f(0) + f'(0)x + 5 (02 2 5()(0) 3 3! 3+ f($) (0 ) 2 ! + ... 4! (a) Find the MacLaurin series expansion for cos(x) up to and including the 26 term. (b) Use your answer from a) to approximate cos(0.9) using the terms up to zo (c) Find the MacLaurin series expansion for ed up to and including the x term. (d) Use the answer from c) to approximate the value of - using terms up to x