Que.1[A] Answer the following multiple choice questions. (K/U) 1. If f (x) sin 3x + cos 2x, then f (x) = a. cos 3x - sin 2x b. 3sin x + 2cos x c. 3cos 3x - 2sin 2x d. 5cos 5x 2. What is the slope of the curve y 2sin x at x = / 3 ?

3. Which of the following is the derivative of y=5x? a. dy/ dx = 5xln 5 b. dy/dx=ex c. dy/ dx=5e5 d. dy/ dx=5(5)x 4. What is the solution to 50 =25 e-2x? a. x = 4 b. x =-1 c. x = 2ln 2 d. x=- ln2/ 2 Que.1[B] determine the derivative of the followings. (15 marks) 1. Y= x^2-3sinx 3. y=cos(sin t) 4. y= x^(-1) cos^(2) . x 5. y=cos(sin t) 6. y= x^(-1) cos^(2) . x 7. y=e^(2x +1) 8. y= 2^x+ 3^x Que.2 Do the following sums.(T/I) 2. Determine d^2. y/(dx^(2)) for y = x^(2) . cosx. 3. Identify the coordinates of any local extrema of the function y=e^x - (e^(-2x)) 4. Find the equation of a line that is tangent to the curve y= 2(3^x) at x=1. Que.3 Do the following sums.(C) 1. Identify the differentiation rule needed in order to find the derivative of each of the following functions with respect to x. a. y = sin x cos x b. y = sin^2 x 2. Consider the function N(t) = (100)2^t , where N(t) represents the number of bacteria in a population after 8 weeks. Why is the initial growth rate of the bacteria not 200 per week ? 3. Let f (x) =e^x and gx=f(x) /f '(x) Which of the following statements do you agree or disagree with? Explain your answer in each case. a) g(x) is a function. b) g(x) is a linear function. c) g(x) is a constant function. d) g(x) is the same function as its inverse. Que.4 Do the following sums. (A) 1. A power supply delivers a voltage signal that consists of an alternating current (AC) component and a direct current (DC) component. Where t is the time, in seconds, the voltage, in volts, at time t is given by the function V(t) = 5sin t + 12. a) Find the maximum and minimum voltages. At which times do these values occur? b) Determine the period, T, in seconds, frequency, f, in hertz, and amplitude, A, in volts, for this signal.

2. Consider a simple pendulum that has a length of 50 cm and a maximum horizontal displacement of 8 cm. a) Find the period of the pendulum. b) Determine a function that gives the horizontal position of the bob as a function of time. c) Determine a function that gives the velocity of the bob as a function of time. d) Determine a function that gives the acceleration of the bob as a function of time. 3. A fruit fly infestation is doubling every day. There are ten flies when the infestation is first discovered. a) Write an equation that relates the number of flies to time. b) Determine the number of flies present after 1 week. c) How fast is the fly population increasing after 1 week? d) How long will it take for the fly population to reach 500? e) How fast is the fly population increasing at this point?