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# Exam1 - Math 213(Fall 2004 Name John Bowman Mon 8:50 Mon...

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Unformatted text preview: Math 213 (Fall 2004) Name: John Bowman Mon 8:50 Mon 12:05 Wed 8:50 Wed 12:05 Yeon Kim Mon 9255 Mon 2:25 Wed 9:55 Wed 2:25 Exam 1 Thursday, October 7, 11:00 7 problems — 100 points — 70 minutes Please write your NAME and circle your SECTION on top of this sheet. Do not detach these sheets. If you run out of space, use the back of the sheets. Show ALL Work for Full Credit NO GRAPHING CALCULATORS may be used on this exam Problem 1 (10 points): Problem 2 (10 points): Problem 3 (15 points): Problem 4 (15 points): Problem 5 (15 points): Problem 6 (15 points): Problem 7 (20 points): Total; 2 1. (10 points) Find the indeﬁnite integral / 33\$ + 3x3 + \$33 + 333 dx 2. (10 points) Evaluate the deﬁnite integral 2 2 IE /____dx 1 213—1 3. (15 points) Evaluate the deﬁnite integral 3 / ln(5:r:) dz; 1 4. (15 points) Compute the areabetween the curves f (:6) = 6"” and 9(33) E e from :c = —1 to a: = 2. 4 5. (15 points) Compute the volume of the solid of revolution formed by rotating the region, bounded by the curves f (:E) = 4 —— \$2 and y = 0, about the m—axis. 6. (15 points) Evaluate the improper integral °°1 2 ~— d V/l x 2\$+1 1‘ Note: The formulas ln(ab) = 111(a) + ln(b) and ln(%) = — ln(a) may be useful. 5 7. (20 points) The rate of change of the volume of water in a dam is given by V'(t) = te“. The initial volume is V(0) = 2 (in millions of liters; time t is in years). (a) Find the volume function V(t). (b) Compute the average volume of water in the lake during the ﬁrst 2 years. ...
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