Show transcribed image text MATH. 241 Sample Exam 2 Fall, 2017 Show your work for full credit and simplify answers when possible 1. Differentiate the following functions a. fr) 37x-3x +4 b. g(θ) = 2sec(8)-Stan(e) c. h(t) = Stzer d. F(u)s suu+2 (Hint: Simplify first.) e, G(w) = _ f, y i. g(x) = ln(V6x7+1) j. h(x) = tan-1(er) k, y = xcos(x) 2. Find first three derivatives of y = 4×2 + 3x-eze 3. Find the slope and the equation of the tangent line to the graph of the function w +2 w2-2 f(x)=xi at the point (1,2) 4. (15 points) At t seconds, an abject in rectilinear motion is s meters fram the orlgin, where s(t) -3t -4t. a. Find the velocity, speed and acceleration of the object at t = 2. b. Is the object moving forward or beckward at this time? Why? ater is leaking out af a swimming pool so that the amount of water remaining in the pool is 5. W s45,000-5t gallons, where t s the number of hours since the pool was filled. At what rate is the water leaking out af the pool when t 3 hours? 6. { 10 points) Find y' = az using implicit differentiation: ye*-z? 7 use logarithmic differentiation to find the derivative of the following function: y = C341)P