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.