Homework 3, Due 10/5

Read sections 2.3 through 2.5 of the text (Thomas/Finney).

Make sure you are able to solve all the core problems in sections 2.2, 2.3, and 2.4.

Learn about MAPLE's "diff" command for taking derivatives; "subs" command for substituting values into expressions. Read the MAPLE manual for these and related worked out problems.

Write up the following problems and hand them in:

Page 129 problems 8, 26, 40, 42.

Page 140 problems 10, 20, 28 (use MAPLE to plot Q(t) on [0,15]; use "diff" to find Q'(t) and then graph it on [0,15]; verify by MAPLE that the rate of draining at t=10 is what you found by hand).

Page 152 problems 8 (find the derivative using MAPLE also and check that it is the same as your own answer), 28, 36, 48, 66.

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BONUS PROBLEM: Let f(x) = x² cos(1/x) if x is non-zero, and f(0)=0. Show that the derivative f'(0) exists and find its value.

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