Assignment 4

Assignment 4 - between the object’s temperature and the...

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Math 138 Assignment 4 Fall 2008 The following questions are to be answered neatly and completely on standard size (8.5 by 11 inch, or metric equivalent) paper. Please insure that your name and ID number are clearly indicated on each page, and that all your pages are securely fastened together, staples are preferred. This assignment is due at 9:00 a.m. on Friday, October 10, 2008 . 1. Use Comparison to determine the convergence or divergence of the following: a) Z 1 x x x + x 2 dx b) Z π 0 sin 2 x x dx 2. Show that every member of the family of functions y = ln | x | + C x is a solution to the diﬀerential equation x 2 dy dx + xy = 1 . 3. Use Euler’s method with step-size 0.2 to estimate y (1), where y ( x ) is the solution to the initial-value problem y 0 = 1 - xy , y (0) = 0. 4. Solve each of the following: a) y 0 = y 2 sin x b) xy 0 + y = y 2 , y (1) = - 1 5. Newton’s Law of Cooling states that the rate of cooling of an object is proportional to the diﬀerence
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Unformatted text preview: between the object’s temperature and the temperature of its surroundings. A cup of coﬀee has tem-perature 95 ◦ C when poured in a room where the temperature is 20 ◦ C . Suppose that we know that the rate of cooling is 1 ◦ C per minute when the coﬀee is 70 ◦ C , solve the diﬀerential equation to ﬁnd an expression for the temperature of the coﬀee as a function of time. Please note that assignments may be submitted to the drop box before the due date. Assignments will be removed from the drop box shortly after the time they are due. The drop boxes are located on the fourth ﬂoor of the Math and Computer building (MC) outside room MC 4066. Check the course outline for the box/slot for your assignment....
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This note was uploaded on 10/21/2010 for the course MATH 138 taught by Professor Anoymous during the Fall '07 term at Waterloo.

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