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Exam_efxam_4_

# Exam_efxam_4_ - MATH 140 EXAM#4 MAY 9 2003 Dr Ellis...

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Unformatted text preview: MATH 140 EXAM #4 MAY 9, 2003 Dr. Ellis INSTRUCTIONS: 1. Write your name and TA’s name on every answer sheet. 2. Answer each problem on a separate answer sheet. 3. SHOW WORK AND GIVE REASONS. NO CALCULATORS. [10] 1. (a) Let ﬁx) =x2—x and let P = {0,%,1,%,2}. Find the lower sum Lf(P). [10] (b) Let g(x) be any continuous function that satisfies —2x 5 g(x) 5 2x for 0 s x S 1. Find upper and lower bounds for I; 1 + g(x) + x2 dx. 2. Evaluate the following integrals. seczx [15] (a) I 10 — tanx dx [15] (b) i an — ex)3/2dx [10] 3. (a) Find the derivative % Ikem’dt. [15] (b) Let ﬂx) = coszx. Find the average value of f on [0%]. [15] 4. (a) Find the area of the region between the graphs of y = x3 + 3x2 + 5x and y = x3 + 2x2 + 7x on the interval [-1,2]. [10] (b) Suppose the velocity of an object is given by v(r) = cos 2r for t > 0. Find the position ﬁt) for t > 0 if ﬂﬂ/4) = 3. mrh25/O3 a:140x4el|isSp03 _...._____—..—_____‘.._L . w ...
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