Read sections 8.11, 10.1, 10.2, and 10.3 of the text
(Thomas/Finney).

Maple work on taylor polynomials. First, work through the maple
worksheet I provided to make sure that you understand what I did.

Consider f(x) = 1/x. 1) Find the first five Taylor polynomials
when you expand about x=1. 2) Consider the interval [1/3,5/3]. Plot
each Taylor polynomial versus f on this interval. Discuss what you
observe. 3) Now find the error bounds E_0, E_1, E_2, E_3, and E_4 for
the interval [1/3,5/3] and plot the errors to demonstrate that they
respect the error bounds. Demonstrate that if you look at the errors
on a larger interval then they can violate the error bounds.

Consider f(x) = sin(x). 1) Find the first nine Taylor
polynomials when you expand about x=0. 2) Consider the interval
[5,5]. Plot the following Taylor polynomials versus f on this
interval: p_0, p_1, p_2, p_3, p_4, p_5, p_7, p_9. Discuss what you
observe. 3) Now find the error bounds E_0, E_1, E_3, E_5, E_7, and E_9
for the interval [5,5] and plot the errors to demonstrate that they
respect the error bounds. Demonstrate that if you look at the errors
on a larger interval then they can violate the error bounds.

Consider f(x) = x^2 exp(x). 1) Find the first five Taylor
polynomials when you expand about x=2. 2) Consider the interval
[1,3]. Plot each Taylor polynomial versus f on this interval.
Discuss what you observe. 3) Now find the error bounds E_0, E_1, E_2,
E_3, and E_4 for the interval [1,3] and plot the errors to demonstrate
that they respect the error bounds. Demonstrate that if you look at
the errors on a larger interval then they can violate the error
bounds.

section 8.11: 4, 12, 44, 52

section 10.1: 9, 16, 20, 28, 30, 38

section 10.2: 11, 16, 28, 42, 53

section 10.3: 8, 16, 20, 25, 32, 45, 52
Problems with Maple? Here are the
commands I used.
For one extra point on the homework, print out and use the homework
cover sheet. This is a *.pdf document that you print and staple to
the front of your homework.
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