A list of extra credit problems which will grow.
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1. Math 215 Calculus IT Extra credit problems This list will grow throughout the semester guidelines When doing an extra credit problem you should write up your solution carefully though I will not collect your write up When you are confident in your solution come see me You will need to talk me though whatever work you have You may present a partial solution to me for partial credit Feel free to ask me questions 1 There is a STEM Science Technology Engineering Mathematics Colloquium Friday March 6 Attend some of the talks and write me something about the topic of one talk 2 Let C be a cone of height h and radius r Compute its volume using calculus 3 Select a geometric figure whose volume formula you might know Use Calculus to derive the volume of this solid Full credit will be given for examples which are interesting and challenging 4 Think about a 4 dimensional sphere of radius r It is given by the inequality etytt 2 wu lt r e What range of values for w can occur in the 4 sphere Find a domain for integration e At any given w What does the defining inequality day about x y and z What is the w cross section What is its 3 dimensional volume e Integrate the 3 dimensional volume of cross sections to find the 4 dimensional volume For full points explain the integration technique used For partial credit use a computer 5 This exercise will guide you through an approximation of 7 1 a Com2. pute 0 1 P za Does this have something to do with 7 1 1 b Using Wolfram alpha approximate J pit Use midpoint approximation 0 and n 100 c Use n 10000 d Use n 1000000 1 e If f t Pal on 0 1 In the error bound on page 510 of the book what value can you take for K g How large must n be if you want an approximation with error less than 107 Have wolfram alpha make this approximation 6 Section 7 8 problem 71 7 Plot the direction field for the differential equation y cos a y and sketch a picture of the solution Using Maple s online user s manual or wolfram alpha s documenta tion or else your own ingenuity run Euler s Method to approximate the solution to y cos x y then what are the maximum value and minimum values of f t 209
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