quiz_08A - Math 213 -- Quiz 8 Name Solution 1. We define...

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Unformatted text preview: Math 213 -- Quiz 8 Name Solution 1. We define the improper integral (over the entire plane R2 ) by I= R2 e-(x 2 +y 2 ) dA = lim a e-(x Da 2 +y 2 ) dA where Da is the disk of radius a and center the origin. Show that I = . Using polar coordinates, e-(x Da 2 +y 2 ) a 2 0 dA = 0 a e-r r d dr 2re-r dr 0 a2 2 2 = = 0 e-u du 2 = -e-a + . Since e-a 0 as a , it follows that I = . 2 ...
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This note was uploaded on 05/09/2008 for the course MATH 2130 taught by Professor Dorais during the Spring '08 term at Cornell University (Engineering School).

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