PDF.js viewer 2022-10-16, 4:26 PM ASSIGNMENT #2 Material covered in this Assignment: MODULES FOUR, FIVE and SIX 1. Draw a rough graph of f(r) = 22 - 1 on the interval 0 0.10-16 4:26 PM 2022-10-16, 4:26 PM 7. Find the following indefinite integrals (show steps): (2 ) (323 + 5 +2') do ( b ) 5 + 2sin I di COS' I 8. A point P moves along the x-axis so that its position x at time t is given by I = 2t3 - 15t2 + 36t + 4. (a) Find the velocity and acceleration of P at time t.20 Question 8 continued (b) Determine each of the following: i. the time interval on which P moves to the right ii. the time interval on which P moves to the left iii. the acceleration when the velocity is zero iv. the average velocity over the time interval [0, 3] v. the acceleration at t - 2.52022- 1 11. Find the domain of In 12. Differentiate each of the following functions. (a) y = [In(x2 - x - 1)]' (b) g(t) = e-3 cos 2t13. Use logarithmic differentiation to find the derivatives of the following: (a) f(x) = 1 + 22 1 + x (b) y = 1(x - 1)2(1. - 2)3. Then evaluate y'|1=3.2022-10-16, 4:26 PM 6 PM 14. (a) A hot object introduced to a cold environment will cool at a rate proportional to the excess of its temperature above that of its environment. If a cup of coffee sitting in a room at a temperature of 20 C cools from 90 C to 40.C in 10 minutes, how much longer will it take to cool to 30.C? (b) Draw a graph of the temperature (C) of the cup of coffee against time (minutes).5 Evaluate the following expressions 1 . l 3 cos c '1' ( ) ( 08 0.4) (b) sin1 (c0370) 16. Differentiate the following functions: 2 1 (a) y = Sin\"1 :1: 3 11: (b) y'f'j'e'i Fage