This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 8:509:40, Sam Eckels, DIS 323, TR 8:509:40, and DIS 330, TR 1:202:10 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 9:5510:45, and DIS 327, TR 11:0011:50,
Dongning Wang, DIS 331, TR 1:202:10 p.m., and DIS 332, TR 2:253:15 p.m.,
Xu Yang, DIS 329, TR 12:05—12:55 p.m., and DIS 333, TR 2:253:15 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). ...
View
Full Document
 Summer '07
 Denissou
 Calculus, Geometry

Click to edit the document details