MATH 1132Q Final: FinalPracticeExam_1132_Fall_2016_Solutions
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MATH 1132Q Full Course Notes
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Important notice: to prepare for the nal exam, study past exams and practice exams, and homeworks, quizzes, and worksheets, not just this practice nal. F beyond its rest length, then 36 ft-lbs of work is done in stretching the spring from its natural length to 6 feet beyond its rest length. Work done stretching the spring from x = 0 to x = 6: = 108 ft-lbs (b) the trapezoid rule with n = 5 for z 4. Justi cation: the curve y = 1/(2x + 1) is decreasing and concave up, so the trapezoid tops lie above the graph throughout. The estimate is larger than the integral. y (c) ln(2. 5) = Xn=1 ( 1)n 1 xn n with radius of convergence 1; the series on the right diverges for |x| > 1. Therefore when we set x = 1. 5, the left side is ln(2. 5) but the right side is divergent.
