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.

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