Name: family name SFU ID: student number (1) Short Answer (8 points) given name SFU email (please print) @sfu.ca (a) (2 points) If the position of a particle at time t is given by s(t) = t3-6t2+2t-4, at what time is the acceleration 0? (b) (2 points) Evaluate lim sin(5x) 2x (c) (2 points) If f and g are differentiable functions, what is & (f(g(x))) ? (d) (2 points) Assume that a radioactive material decays according to the formula N(t) = Noe-kt. Write a formula for the half-life. 1
(2) Short Answer (8 points) (a) (2 points) If y = sin(2x) what is y"'? (b) (2 points) Evaluate lim (1 + 1)3n n-100 (c) (2 points) Let f be a function differentiable at x and let Ax = da be a (small) number. What is the formula for the differential dy? (d) (2 points) Express the following in the form of an equation: "y is a quantity which increases at a rate proportional to its size" 2
(3) (12 points) Differentiate the following functions sin x + 10x (a) (3 points) y = e3x (b) (3 points) y = sin(cos(3.x)) (c) (3 points) y = 2ª3 (d) (3 points) y = (sin.x)(cos x)(tanx) e3= (x2+1) 3