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1. If f(x) = sin (x), find f a. 0 C. b. 1 d. 2. If f(x) = Sin X find f * COS X a. 1 C. b. -2 d. 2 3. Find the slope of the tangent to the curve y = 2 sin'x at x = a. C. -1 b. 3 d. 4. Find the slope of the tangent to the curve y = 3x cos x at X = I. a. -3 C. 3 b. 0 d. 6 5. Find the slope of the tangent to the curve y = 4 sin 2x at x = a. -3 C. 31/3 2 b. 6 d. 9 6. Ify = 2 cos x + sin 2x, find y" at x = a. N C. b. -67. Ify = 2 sinx - cos x, find y" at x = a. 1+ 3 C. 1-2-3 2 2 b. 1- /3 d. 1+2 43 2 2 8. Ify = sin 3x 9 , find y" at x = a. 1 C. 0 b. -1 d. 2 9. Find the slope of the tangent to y = 1 - 2 sin x at the point where x = a. c. 2 b. -1 d. -2 10. If f(x) = sin 3x, find a. 3 C. 9 b. -3 d. -9 11. If f(x) = cos (nx) - sin (nx), find f An a. -8m 83 b. -8 d. -4m 12. Find f '(x) if f(x) = 2e*. a. 20* C. e In2 b. e* d. 2e 13. Find the equation of the tangent to y = e"at the point (0, 1). a. V = X+ I C. Y= ex+ 1 b. y=-x-1 d. y= x+1 14. Iff(x) = 2x e*, find f'(1). a. 2e 0 b. be d. 15. Find the equation of the tangent to y = 3e + 3ex that is parallel to y = 6ex + 5. a. bex- y = 0 C. bex- y = 68 b. 6ex+y = 0 d. bex+ y = bePart 3: Thinking [11 marks] 2?. Differentiate the following. a} y 2 4I [1 mark] b] y 2 51:2" [1 mark] 5] J' = '3 ESSEX} [2 marks] d] y = sin(x x2) cos (i) [2 marks] I e) y = ecos(*) sin(2x - 1) [2 marks] 28. The displacement of an object attached to the end of a spring can be modelled by the function h(1) - 2.4cos 12t+ , where h is the height of the object from the floor, in centimetres, and t is the time, in seconds. Determine the acceleration of the object at time t. (3 marks)Part 4: Application [12 marks] 29. Find the equation of the tangent to the curve y = 4x - tanx at the point where x - . [6 marks] 30. The population of a bacterial culture was 5000 bacteria after 15 min and 40 000 bacteria after 1 h. a) After how many minutes will the population reach 150 000 bacteria? (3 marks) b) Find the rate of growth after 15 min. Express your answer as bacteria per hour