Instructions: the exam is closed book and closed notes. You may use an approved calculator, but be sure to show your work on each problem for full credit. Work that is crossed out or erased will not be graded. Turn in any scratch paper that you use during the exam. You will have one hour and 45 minutes to work on the exam. Show all of your work. (a) z 5x4 + 2x2 x3. + dx (b) z t3 sin(t4 + 7)dt (c) z 1. 3 (2x + 1)3 dx (d) use integration by parts to evaluate z 5xe4xdx. 2: (14 points) consider the discrete-time dynamical system. Find the value of h that maximizes p (h). Use the rst or second derivative test to justify that this value of h gives a local maximum. (c) use the stability test/criterion to determine if the equilibrium you found in (a) is stable if h = 1.