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M137.F07.Assign8

M137.F07.Assign8 - Math 137 ASSIGNMENT 8 Fall 2007 Submit...

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Unformatted text preview: Math 137 ASSIGNMENT 8 Fall 2007 Submit all boxed problems and all extra problems by 8:20 am. November 16. All solutions must be clearly stated and fully justiﬁed. Use the format given on UWACE under Content, in the ﬁle Assignment Format for Math 135 and Math 137. TEXT PROBLEMS: Section 4.1 — 3, 5, 9, 13, 25, ,I, 49, I, I, 62, m [Use the Closed Interval Method on page 275 for problems 49—73.] Section 4.3 — 5, 7, 11, 17, 25, 31, 39, I, [Go through the odd-numbered problems using the Homework Hints in TEC at wwwstewartcalculus. com] Section 4.5 — 9, 19, 33, .(on ~7r 3 ac g 71'), 41, I, [Use the 8—step method A—H on pages 308—309 for sketching graphs] Section 4.7 — 7, 9, I, 13, 17, I, 30, 33, 37, I, 49 [Problems 12 and 42 involve optimization on an open interval I . You can test ‘end—point’ behaviour by considering the limiting values (from inside I ), and/ or using the First Derivative Test to determine the nature of any critical numbers in I. For problem 22 use the Closed Interval Method] EXTRA PROBLEMS: E8.1* Telegraphs were originally transmitted in Morse Code, a series of short (dots) or long (dashes) signals representing the letters of the alphabet. If the fraction of dots and dashes per unit time are a: and 1—x respectively, where 0 < x < 1, then the information content is given by [(93) = —xlnx —— (1 —— as)ln(1 — :13). a) Show that [(1') > 0. b) Find the value of m which maximizes [(1) c) Discuss brieﬂy how the result in b) might be useful. ...
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