Yorkdale Adult Learning Centre MCV 4UV - Mathematics , Grade 12 Calculus and Vectors Quad 4 (April 2023 - Jun 2023) Name: Date: Jun 7, 2023 Test 4 K/U /10 A /10 T 18 C 14 Note: Answer all the questions. Show your work for all questions. 1. (K1+2+2 +2 Marks) a) If f(x) = xe" , find f'(0). b) If f(x) = sin( e" ), find f'(0). c) Differentiate f(x) = d) If f(1) = In(312 + (), determine f'(2). 2. [K 3 Marks} I Find the equation of the tangent to the curve _I' : use: .1: at the point where x - 3 . (Note: Work with fractions and leave the answer in the exact form. in terms of 11'.) 3. [A 2 Marks] v2 The range ot'a projectile can be modelled by the function R - E] sin 31. where v is the initial speed in metres per second, 3 is the gravitational acceleration, in metres per second squared. and .r is the angle to the ground. Determine the function that measures the rate ot'ehange of the range with respect to the angle of thrust. [ A 2 Marks] A ball bearing moving through oil in an experhneut has the position function y - tttr+ 8t?" . Determine the velocity function of the ball bearing