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Wednesday, February 10 Announcements WeBWorK #5 is due tonight at 9pm Pick up your quiz papers in the Math Learning Centre Quiz #3 will take place here on Friday, February 12 (second half of class time) Covers material from Week 4 and Week 5 As usual: no notes, no scratch paper, no phones, no calculators, etc. You must bring your student ID to class on every quiz day You must take the quiz in the section you’re registered in Thank you for your cooperation with the exam-conditions procedures (especially staying in your seats, and not talking, until all quiz papers have been collected). It helps us a lot! and keeps the quizzes efficient. Wednesday, February 10 Clicker Questions Clicker Question 1 Not much of a puzzle Which of the following indefinite integrals do we know how to evaluate? Z 1 1 (u = 7x + 9) A. dx = log |7x + 9| + C 7 7x + 9 Z 1 1 1 B. dx = +C (u = 7x + 9) 3 (7x + 9) 7 (−2)(7x + 9)2 Z 1 dx = arctan x + C C. x2 + 1 Z x 1 D. dx = log |x2 + 1| + C (u = x2 + 1) 2 x2 + 1 E. all of the above The purpose of partial fractions is to use algebra to rewrite complicated rational functions as combinations of simple pieces like these, to make integration much easier. Clicker Question 2 Fraction with a fancy numerator Find constants A, B such that A. A = 19, B = 38 B. A = 8, B = − 52 A B 16x3 + 35 = + . 2 2x + 5x + 3 x + 1 2x + 3 Why don’t they exist? C. A = 8, B = −20 We’re being asked to find constants that satisfy D. A = 19, B = −22 16x3 + 35 = A(2x + 3) + B(x + 1); E. no such constants exist but the degree of the left-hand side is too large for that to happen.