217-zhu-07sp01

# 217-zhu-07sp01 - MATH 217 MIDTERMI(SPRING 2007 Name Section...

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Unformatted text preview: MATH 217: MIDTERMI (SPRING 2007) Name:____-______________________-________ Section: _---_______ TA:__________________ Score: Problem 1 _________________________ _. Problem 2 __________ _; ______________ __ Problem 3 __________________________ -_ Problem 4 __________________________ __ Problem 5 _________________________ __ Total: _________________________ __ Instruction: Show all work. No work = no credit, even if you have a correct answer. References and calculator are not allowed. Problem 1 (20-points): Consider the function f = 12:3 + 33:2 — 9x + 1 deﬁned on (—oo,oo). ‘ (a) Determine in Which intervals the function is increasing, decreasing, con- ' cave up-and concave down. v (b) Determine all local maximal and minimal values of f. Justify why they are local maximal or minimal values. [\3 Problem 2 (5 points): Use L’Hospital’s rule to evaluate , sinus — sin 3333‘ 11m 96—0 x/l—i—m—l Problem (20 points): Evaluate the following indeﬁnite integrals; (a) (6 pomts) f(2x + i + ﬁﬂiﬂ: (b) (6 points) f(cos(2:c) — sec :10 tan a: + 3)dx (c) (8 points) fx2(2 + x3)9dg; Problem 4 (15 points): Find the area between the graph of the function f(x) = (—Izgf—ﬁ and the sis—axis over the interval [0,1]. Then ﬁnd the average value of the function on this interval. 0! Problem 5 (10 points): Evaluate the folloWing limit by writing it as a deﬁnite integral and then evaluate that integral. Make sure you show some justiﬁcation for the deﬁnite integral you are using. sin(ZT:-) + sin(-2n1)+---+ sin(1‘1—:5) n-—>+oo ‘ n ...
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217-zhu-07sp01 - MATH 217 MIDTERMI(SPRING 2007 Name Section...

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