advertisement

Name Student ID # Math 1320 Spring 2014 SAMPLE EXAM I This is only to give you a general idea of what to expect. The actual exam may or may not include problems similar to those given here, and it may be longer or shorter. Instructions: Show all of your work for full credit. Problem 1. 2. 3. 4. 5. Points 20 20 20 20 20 TOTAL Score (20 points) 1. Find the volume of the solid obtained by rotating the region bounded by the curves x = cos y, y = 0, y = π/2, about the x-axis. (20 points) 2. Find the work required to lift a 500 lb container of drywall from ground level to the top floor at 400 ft. The container is pulled by a cable which weighs 2 lb/ft. 1 (20 points) 3. (a) Solve the initial value problem dy 2xy = 2 , y(0) = 1. dx x +1 (b) Use Euler’s Method with step size 0.1 to estimate y(0.3). 2 (20 points) 4. A cup of coffee is poured at 180 ◦ F, and placed on a desk in a 70 ◦ F room to cool. After 5 minutes, the coffee is at 140 ◦ F. How long after pouring will it take for the coffee to reach 90 ◦ F? (20 points) 5. Find the radius of convergence and the interval of convergence for the ∞ X (2x − 2)n (−1)n √ power series . n+1 n=0 3