homework 10

Homework 10, Due Friday 11/17 (for everyone)

Read sections 4.6, 4.7, 4.8, and 4.9. of the text (Thomas/Finney). I will not be covering 4.9 in class, but you will be responsible for the material anyway. It's material that's best understood by "doing".

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

Here's a sample worksheet where I coded up and used the Trapezoidal rule and Simpson's rule: sample worksheet for help.

Problems with Maple? Here are the commands I used.

A hint on making your maple life easier: make seven copies of my maple worksheet, prob1.mws, ..., prob7.mws This willl save you a huge amount of typing since you can make minor modifications of prob1.mws and prob2.mws to do the trapezoidal rule problem and minor modificiations of prob3.mws, ... prob7.mws to do the integrability problems.

Do the following problems in maple and hand in your print-outs. These problems will be graded, so make sure to do it!

You've done problem 8 of section 4.9 as the book instructed. Now do the following with the same integral:

Now we switch directions and look at integrability. In class, I claimed that if you try to integrate 1/x over [0,1] then the Riemann sums go to infinity. I also claimed this about the Riemann sums for 1/x^(1.001) and 1/x^2. In the worksheet, I test the case of f(x) = 1/sqrt(x). It blows up at x = 0, but it's actually integrable on [0,2]. It's integrable on [0,b] for any b.

Warning! Read the problems below carefully! Make sure that you notice whether you're reading "is" or "is not" and be careful about what interval the integration is over.

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