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Unformatted text preview: | b) One example f ( x,y ) = p | 1-x 2-y 2 | B6. f ( x,y ) = | x | . B7. u x ( 3 4 , 1) =-100 π e √ 2 , u t ( 3 4 , 1)-100 e √ 2 B8. u t represents the rate of change of the displacement with respect to time. i.e. if we look at a ﬁxed point x on the string, it measures the rate of change of the displacement of the string at that location at that time. u x represents the rate of change of the displacement with respect to position. i.e. at a ﬁxed time, it measures the rate of change of the displacement of the string if you move along the string from some point. 1 2 B9. The volume decreases by 12 . 5 π m 3 . B10. The approximate change in R is 55 . 123966 ... ohms. Actual, 55 . 1246 ... ohms. B11. The planes are z =-4-4( x-2)-2( y-1), and z = 4 5 + 4 5 ( x + 2 5 ) + 2 5 ( y + 1 5 ). B12. b) c , c) u ( x,t ) = Ae-( x + ct ) 2 C1. C3....
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This note was uploaded on 11/30/2010 for the course MATH 235/237 taught by Professor Wilkie during the Spring '10 term at Waterloo.
- Spring '10