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Unformatted text preview: Name: TA: Math 20B. Midterm Exam 2 February 26, 2007 Sec. No: PID: Sec. Time: Turn off and put away your cell phone. No calculators or any other devices are allowed on this exam. You may use one page of notes, but no books or other assistance on this exam. Read each question carefully, answer each question completely, and show all of your work. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clarification. 1. (a) (4 points) Compute (1 + i)7 , and express your answer in the form a + ib. (b) (2 points) Compute (1 + i)7 , and express your answer in the form a + ib. # 1 2 3 4 5 Points 6 6 8 5 5 30 Score 2. (6 points) Displayed below is the graph of an ellipse x2 y 2 + = 1. After solving for y, a2 b2 x2 one finds the upper half of the ellipse is the graph of y = b 1  2 . Find the area a enclosed by the ellipse using integration. (Hint: find the area in the first quadrant and multiply by 4.)
b a 3. Evaluate the following indefinite integrals. (a) (4 points) x 2 ln(x) dx
3 (b) (4 points) x+1 dx x2  2x 4. (5 points) A radar gun was used to record the speed (in meters per second) of a runner during the first six seconds of a race; the data is recorded in the table below. Estimate the distance the runner traveled during the six seconds using the Midpoint Rule with three subintervals. Be sure to determine which subintervals you will use to apply the Midpoint Rule. Time (sec) Velocity (meters/sec) 0 0 1 2 3 4 5 6 7.3 9.7 10.5 10.7 10.8 10.8 5. (a) (1 points) Explain why the integral
0 2 1 dx x+2 is improper. (b) (4 points) Evaluate the improper interval in part (a), or show that it diverges. ...
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 Spring '08
 Justin
 Math, Calculus, #, Midpoint Rule, 2007 Sec

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