Wednesday, March 30
Announcements
WeBWorK #11 is due tonight at 9pm
Quiz #5 grades: our section’s average was 5.4/10
Submit any Quiz #5 regrade requests by Monday, April 4
Quiz #6 will take place here on Friday, April 1 (second half of
class time)
Covers material from Week 10 and Week 11
Usual rules: closed book, bring your student ID, take the
quiz in your own section, stop writing when told to do so
Thank you for your cooperation!
I will not be here on Friday. Dr. Lim (another MATH 101
instructor) will give the half-lecture and administer the quiz.
He’s doing our class a favor—treat him (at least) as nicely
as you treat me!
Wednesday, March 30
Clicker Questions
Clicker Question 3
New power series from old
Find a power series representation, centred at 0, for the
function log(1 − x).
x2 x3 x4 x5
− − − −···
2
3
4
5
3
4
2
x
x
x5
x
+
−
+
− ···
B. x −
2
3
4
5
C. x + 2x2 + 3x3 + 4x4 + 5x5 + · · ·
A. −x −
D. x − 2x2 + 3x3 − 4x4 + 5x5 − · · ·
E. none of the above
Integrating a power series
∞
X
1
=
xn
1−x
n=0
Z
1
dx
− log |1 − x| =
1−x
∞
X
xn+1
=C+
.
n+1
n=0
Plug in x = 0 on both sides
to get C = 0.
Clicker Question 2
Related series
P
n
Suppose that the series ∞
n=3 cn (−6) converges. What can we
say about the radius of convergence, R, of the power series
∞
X
cn n(n − 1)xn−2 centred at 0?
n=3
A. R = 6
Double derivative
B. R ≤ 6
P
n
Let f (x) = ∞
n=3 cn x ; since the series
converges at x = −6, its radius of
convergence
6. But
P∞ is atnleast
P
00
00
n−2
f (x) = n=3 cn (x ) = ∞
n=3 cn n(n − 1)x
has the same radius of convergence as the
series for f (x) itself; so R ≥ 6.
C. R ≥ 6
D. |R| = 6
E. none of the
above