homework 2
## Homework 2, Due Wednesday 9/20 (for those in Tuesday recitations) and on
Friday 9/22 (for those in Thursday recitations)

Read sections 1.1 and 1.2
of the text (Thomas/Finney).

Make sure you are able to solve all the core problems in
these sections.

Get to learn the basic commands in MAPLE as they are an important
element in this course. Commands you should know about
for this week's assignment are "plot", "diff", and "limit".

Write up the following problems and hand them in:
section 1.1, page 57: 7, 9, 13, 17, 35
(in both 13 and 17, do the plotting in maple and present
the
plot on at least three scales, zooming in to x=-6 and x=0, respectively.)

section 1.2, page 65: 9, 17, 27, 31, 33, 43, 45

Do the following problems in maple and hand in your
print-outs. Go through the
*
sample worksheet * for help. Save the worksheet, 9_13_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
printing it.)

For further guidance, see pages 13-35, 40-46, 68-71, 83-85, and 86-89
of your maple lab manual.
Plot sin(x), sin(2x), sin(3x) on the same plot, over the interval
[0,2*Pi].

Plot x*sin(x), x^2*sin(x), x^3*sin(x) on the same plot, over
the interval [-.1,.1] and over the interval [-2,2]. Which are the
even functions, and which are the odd functions?

Define the function f, f(x):= x-> 2*x^2 + 1. Find the average
velocity av_vel = (f(x0+h)-f(x0))/((x0+h)-x0). What is its limit as
h->0, as found using the maple command "limit"? Compare this to the
derivative of f, as found using the maple command "diff".

Define the function f(x):= x-> (x^2-4)/(x-2).
What is its limit as
x->2, as found using the maple command "limit"? Plot the function and
verify the limit visually. Evaluate f at 2.

*Back to
Math 140*