Homework 3, Due Wednesday 9/27 (for those in Tuesday recitations) and on
Friday 9/29 (for those in Thursday recitations)
Read sections 1.4, 1.5, and 1.6
of the text (Thomas/Finney).
Make sure you are able to solve all the core problems in
Write up the following problems and hand them in:
section 1.4, page 83: 6, 10, 18a, 20a, 30, 36, 46, 48, 50
section 1.5, page 95: 8, 20, 28, 34, 40, 46, 50
section 1.6, page 101: 18, 22, 24, 26, 28, 32, 34
Do the following problems in maple and hand in your
print-outs. Go through the
sample worksheet for help. Save the worksheet, 9_20_00.mws,
on your floppy disk. Open maple by clicking on the maple icon on the
windows desktop. Then open the worksheet by clicking on the "file"
pulldown tab, selecting "open", and finding the worksheet on your
floppy disk. Work through the worksheet from top to bottom. In the
process, you should learn everything you need to do the following
problems. Print it out so it's handy for you when you do your
homework. Now open a new worksheet to do your homework and print it
when you're happy with the results. Note: you can save your work as
HW1.mws (for example), go off and have dinner, and then resume your
work by reopening HW1.mws. When you've done all the problems, trim
out the stuff you don't want to hand in, print it out and add comments
by hand. (Or you can type your comments into the maple session before
Problems with Maple? Here are the
commands I used.
Consider f(x) = exp(cos(x)) at the point 2*pi. Find three right
secant lines and three left secant lines. Take them with h=1/2, 1/4,
and 1/8 (for the right ones) and h=-1/2, -1/4, and -1/8 (for the left
ones). Plot the function and the right secant lines on three
different scales, zooming in to show how well they're fitting the
curve. Plot the function and the left secant lines on three different
scales, zooming in to show how well they're fitting the curve.
Discuss what you observe.
Consider f(x) = sqrt(x^2-4x+3) at the point 3. Find six right secant
lines. Take them with h=1, 1/2, 1/4, 1/8, 1/16, and 1/32. Plot the
function and the right secant lines on three different scales, zooming
in to show how well they're fitting the curve. Discuss what you