If the WeBWorK gives you troubles, for example it "loads" forever, please let me know and use
one of these links instead of the one above:
http://bakura.math.nau.edu/webwork2/JSwift_137/
http://kuat.math.nau.edu/webwork2/JSwift_137/
Here is a picture of some partial sums of the power series
ln(1+x)
= x - x2/2+x3/3 - x4/4 + ... .
The series converges iff -1 < x <= 1.
Here is a picture of some partial sums of the power series
1/(1+x2)
= 1 - x2 + x4 - x6 + x8 - ... .
The series converges iff -1 < x < 1.
Here is a picture of some partial sums of the power series
arctan(x)
= x - x3/3 + x5/5 - x7/7 + x9/9 - ... .
The series converges iff -1 <= x <= 1.
Here is a picture of some partial sums of the power series
cos(x)
= 1 - x2/2 + x4/4! - x6/6! + ... .
The series converges for all x.
Extra Credit, Due April 6
The series sum from 2 to infinity 1/(n ln(n)) diverges. (The integral test shows this.)
Estimate the k for which kth partial sum is equal to 10. (The kth partial sum
is sk = sum from 2 to k+1 of 1/(n ln(n).)
I will give you 5 extra credit points if you can estimate k to within a factor of one million.
I will give you 2 class points if you can estimate k to within a factor of googol (10^100).
In other words, find k1 and k2 such that the partial sums satisfy s_k1 < 10 and s_k2 > 10 and k2/k2 < 10^6 (for 5 class points) or
k2/k1 < 10^100 (for 2 class points).
Hint: it is known that s_googol < 6.3 and s_googolplex > 231, where
googolplex is 10^googol, not to be confused with
Googleplex, the corporate headquarters of Google, Inc.
Thus k1 = google and k2 = googleplex satisfy s_k1 < 10 < s_k2, but k2/k1 is too large to get extra credit.
Hint: Choose an n and compute s_n. Then estimate the rest of s_k using an integral.
Graph of the two sequences associated with the
geometric series
(2/3) + (2/3)2 + (2/3)3 + ... = 2.
Graph of the two sequences associated with the
harmonic series
1 + 1/2 + 1/3 + 1/4 + ..., which diverges.
Here is the Mathematica notebook that made these graphs.
If you can run Mathematica, you can define your own sequence of terms an for the sum.
You can run Mathematica using the CEFNS Secure Global Desktop.
Extra Credit worth up to 5 class points: Due in class Monday, March 23. (Copyright 2009, The Mathematical Association of America)
Ten women sit in 10 seats in a line. All of the 10 get up and then reseat themselves using all 10 seats,
each sitting in the seat she was in before or a seat next to the one she occupied before. In how many ways can the women be reseated?
Euler's method handout from class on Feb. 25.
Marek Rychlik's Slope Field Applet, at Eduardo Sontag's web site.
Here are some Mathematica notebooks about the average value of functions:
fAverage.nb, fAverage2.nb,
and fAverage3.nb.
These teach you how to "eyeball" the value of a definite integral from the
graph.
You can run Mathematica using the CEFNS Secure Global Desktop.
Figures relevant to WeBWorK set 10_Length_Ave problem 3
Figures of catenaries. "Catenary"
comes from the Latin word for "chain".
Figures of y = cosh(x),
y = -cosh(x). Another figure
of y = cosh(x). What's
different?
The hyperbolic sine and cosine are defined by
Page with figures for improper integrals.
Here are some places to get help as you review Differentiation and Integration skills:
Differentiation Shortcuts
Review of Calculus I
Visual Calculus by Lawrence S. Husch at
Knoxville. This has some good tutorials.
Solutions to the handout on the first day.
The free on-line interactive text, by Paul Dawkins of Lamar University.
Here is a link to NAU policy statements. These math department policies are part of the printed syllabus for our course, but are not in the on-line version of our syllabus.
Introduction to WeBWorK at NAU
COMPUTER LAB OPEN HOURS --- AMB 222
M-Th 9:00am - 5:00pm, F 9:00am - 4:00pm,
except when the lab has been reserved at least a day in advance for use by a class.
You can go there before or after class with your friends and work on WeBWorK together.
