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221-seeger-07faex03

# 221-seeger-07faex03 - Math 221 Midterm Exam III Please note...

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Unformatted text preview: Math 221 Midterm Exam III, October 24, 2007 Please note: There are seven problems (each worth 14 or 15 points) and an extra credit problem (no. 8). ’ YOUR NAME: Circle the name of your TA and discussion: Eric Andrejko, DIS 326, TR 11:00—11:50, and DIS 328, TR 12:05—12:55, Erkao Bao, DIS 321, TR 7:45—8:35, and DIS 322, TR 8:50-9:40, Sam Eckels, DIS 323, TR 8:509:40, and DIS 330, TR 1:20-2:10 p.m., Hongnian Huang, 'DIS 324, TR 9:55—10:45, and DIS 334, TR 3:30—4:20 p.m., Seyﬁ Turkelli, DIS 325, TR 9:55-10:45, and DIS 327, TR 11:00-11:50, Dongning Wang, DIS 331, TR 1:20-2:10 p.m., and DIS 332, TR 2:25-3:15 p.m., Xu Yang, DIS 329, TR 12:05—12:55 p.m., and DIS 333, TR 2:25-3:15 pm. Scores: No. 1: (max 15 points) N0. 2: . (max 14 points) No. 3: (max 14 points) No. 4: (max 14 points) No. 5: (max 14 points) No. 6: ' . (max 15 points) No. 7: , (max 14 points) Exam Score: Extra Credit: 1. (15 pts.) Let 0 if m < 1 f(a:)= —2 if1_<_a:<3 a: —- 5 if a: Z 3 Sketch the graph of f and compute 6 f(x)d:1;. 1/2 2. (14 pts.) Find a function A'so that A’ (:13) = mcosm for all no and A’ (0) = 1. 3. (14 pts.) Let ’R be the region in the plane which is bounded by the curves y = 3x and y = — cosx and the vertical lines :3 = 0 and a: = 7r/2. ' Sketch ’R, and compute its area. 4. (14 pts.) Compute for every M the integral M 4 » 5 / ‘ac cos(:c )+ 43: d9; 0 3 5. (14 ptS.) . v Consider the curve deﬁned by y = 233/2, for a: between 1 and I) (here b > 1). Make a sketch and compute the length of the curve. ’ 7. (14 pts.) Compute the derivative of ' I 2+cosx 11(13): v1+t3dt. 1 8. (Extra credit problem). Properly state and prove part 1 of the fundamental theorem of calculus (which is about differentiating an integral of the form f: f (t)dt). ...
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221-seeger-07faex03 - Math 221 Midterm Exam III Please note...

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