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Unformatted text preview: . CALCULUS 222
6th WEEK EXAM I. M. Isaacs
Thursday, March 1, 2007
5:30 — 7:00 PM. I Do all problems # 100 points.
Use backs of pages for scrap, or if you need more space. NAME: TA: Do not write below here. Prob. 1: out of 26.
l Prob. 2: I out of 26.
Prob. 3: out of 10.
Prob. 4: . out of 10.
Prob. .5: V out of 20. Prob. 6: _____ out of 8. Total: out of v 100. 1. [26 POINTS] Integrate each of the following. (b3 /_x21n(:c)da: ‘ 2. [26 POINTS] Here are two more integrals to compute. (a) /4a:4+1dx 41:3—113 (b) / sin(ln(ac)) d9; 3. [10 POINTS] Use Simpson’s rule with four intervals to ﬁnd an approximation for ln(3). HINT: Start by writing a simple integral Whose value is 1n(3). WOrk with fractions, not decimals.
1 NOTE: ln(3) 7:: 1098612289. You can use this to check that your answer is reasonable. 4. [10 POINTS] Decide Whether or not this integral has a meaningful value. If it does, compute
the value and if not, explain Why not. L 5. [20 POINTS] Solve these two initial value problems.
(a) y’ + tan(x)y = sec(a:) for —7T/2 < 2: < 7r/2. y = 3 when a: = 0. MW
(b) 3yy” = 2(y’)2. y = 1 and y’ = 3 when :1: = 0. 6. [8 POINTS] Find the general solution of this differential equation. y" — 61/ + 9y =91: THE END ...
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This note was uploaded on 08/08/2008 for the course MATH 222 taught by Professor Wilson during the Fall '08 term at University of Wisconsin.
 Fall '08
 Wilson
 Calculus, Geometry

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