ue.1[A] Answer the following multiple choice questions.(K/U) 1. Which is the second derivative of the function y= -cos x with respect to x? a. d ^2y/dx^2=sinx b. d ^2y/dx^2=-sinx c. d ^2y/dx^2= cosx d. d ^2y/dx^2= -cosx 2. If g(x) =3cos 2x, then g (x) = a. 6cosx b. -6sinx c. -6sin2x d. -6cos2x 3. What is the value of ln (e ^(-2x))when x =2? a. e^(-4) b. ln(-4) c. -4 d. -2e^-2 4. What is the derivative of f (x) = e-x cos x? a. f'(x)= -e^(-x)(cosx + sinx) b. f'(x)= -e^(-x)(cosx - sinx) c. f'(x)= -e^( -x)(sinx - cosx) d. f'(x)= -e^(-x )sin 2x Que.1[B] determine the derivative of the followings. 1. Y= cosx + 2x +2inx 2. f()=/2 + 3. f(t)= sin^2(cost) 4. f(t) = 3tsin^3 . (2t-) 5. e^(2x) -e^ (-2x) Que.2 1. Do the following sums.(T/I) find the equation of the line that is tangent to the function y= -4sinx at x=/ 2.Use algebraic reasoning to explain why the function y= e^x+e^(2x) has no local extrema. 3. a) Determine the derivative of f (x) = sin 2x with respect to x. b) Determine the derivative of g(x) = 2 sin x cos x with respect to x. c) Show that the derivatives in parts a) and b) are equal. d) Explain why the derivatives in parts a) and b) should be equal. 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 . Justify your answer. a. y=2e^x+x^2 b. f(x) = e^(-2x+3) c. y= e^(2x)x^3 2. explain the difference between natural logarithm and common logarithm. 3. Let f(x) =xsinx. Describe the steps you would use to find f'() Que.4 Do the following sums.(A) 1. The voltage signal from a standard North American wall socket can be described by the equation V(t) =170sin 120t, where t is time, in seconds, and V(t) is the voltage, in volts, at time t. a) Find the maximum and minimum voltage levels, and the times at which they occur. b) For the given signal, determine c) i) the period, T, in seconds ii) the frequency, f, in hertz iii) the amplitude, A, in volts 2. A student grew bacteria in a petri dish as a science project. He estimated the initial population as 1000 bacteria. After 1 day, the population N was estimated to be 1500 bacteria. Assume that the bacterial growth follows an exponential relation of the form N (t)=Noekt. Determine the values of Noand k, assuming that t is measured in days. a) How long will it take for the population to double to 2000 bacteria? b) Differentiate the population function with respect to t. c) How fast is the population growing at t = 5 days