213-chen-07spex01 - Calculus and Introduction to...

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Unformatted text preview: Calculus and Introduction to Difierential Equations Math 213 Exam One Instructor: J unChen No calculator allowed.» ‘Write detailed work to obtain full credits. Your Name: Please circle your TA session: TA NAME ' Thursday Hu Zheng _12=05pm 12:05pm 14:25pm 14-25mm Problem/pt Pl/ZO P2/20' P3/25 ‘P4/l5 P5/20 Total 1. (20 pt) Suppose a car travels at speed 12(55), Where some data of the speed are given by the following table: _---n Speed 11(m) (Miles / Hour) Estimate the distance the car travels from time cc = O to x = 4 by the following methods: (a) Trapezoidal rule (10 pts) with n = 2; (b) Simpson’s rule with n = 4(10 pts). (Compute the final answers as one number for each part) ' 2. Evaluate the following integrals (simplify the answers if possible): (a) (10 pts) [02w — e-xm (b) (10 pts) ff (3%fidx. 3. Use integration by parts to compute the following integrals (simplify the answers if possible): (a) (10 pts) folacezxdsc. (b) (15 pts) f13(ln$)2dx 4. (15 pts) Find the volume of the solid of revolution formed by rotating about the y-axis the region bounded by y = fl, y—axis and y = l. 5. (20 pt) Suppose the rate of a money flow is f (cc) = 100605” dollars per year. The annual interest rate is 10%. (a) (7 pts) Compute the accumulated amount of the money flow at time t = 5. (b) (13 pts) If the present value for 75 years is 400 dollars. Calculate the time period t (expression 'can inVolve 1n). ...
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