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Unformatted text preview: t , given by ( x,y,z ) = ( t 2 ,t sin t, cos t ). The temperature T = T ( x,y,z ) satises T ( 2 , ,1) = (1 , 2 ,1). [Recall that T = ( T x ,T y ,T z ).] Compute the rate at which the ys temperature is changing at t = . State any assumptions required in your computation. 4. Let f ( x,y ) = xe xy , and suppose x = x ( s,t ) = ( s + 2 t ) 2 and y = y ( s,t ) = sin( st ). (a) Find f s and f t . (b) Find f ss and f tt . 5. Let f,g : R R be twice dieretiable, and R . Show that u ( x,t ) = f ( xt ) + g ( x + t ) satises the wave equation u tt = 2 u xx 6. Let g : R R , and f ( u,v ) = g ( uv 2 ), where u = u ( x,y ) = ( x + y ) 3 and v = v ( x ) = 1 x . Calculate 2 f yx . State any assumptions required in your computation....
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This note was uploaded on 10/19/2011 for the course MATH 237 taught by Professor Wolczuk during the Spring '08 term at Waterloo.
 Spring '08
 WOLCZUK
 Math, Approximation, Linear Approximation

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