MATH 101 Study Guide - Quiz Guide: Trapezoidal Rule, Atan2, Riemann Sum
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1 5q (t1 5q 1) with 1 5q > 0, t5q 1 ) with 5q 1 > 0, 5q 1(1 1 log t, if q < 1. 1 5q (limt t1 5q 1) = , limt log t = , 5q 1(1 limt 1 t5q 1 ) = 1. Thus the total error for the trapezoid rule with n = 90 points is bounded by. Solution: let x = 5 tan , so that x2 + 25 = 25 tan2 + 25 = 25 sec2 and dx = 5 sec2 d . (cid:90) (cid:90) 1 (25 sec2 )3/2 5 sec2 d (cid:90) 125 sec3 d cos d sin + c = Marking scheme: x2+25 when tan = x. 3x2 4 (x 2)(x2 + 4) dx. 8 = 12 4 = (4 + 4)a = 8a a = 1. 3x2 4 (x2 + 4) = (x 2)(bx + c) b = 2, c = 4. 3x2 4 (x 2)(x2 + 4)
