Quiz 4 KEY

Quiz 4 KEY - f x ( x, y ) =-2 x sin( x 2 + y 2 ), so that f...

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Name: PID: TA: Sec. No: Sec. Time: Math 10C Quiz 4 March 7, 2008 1. Given z = f ( x, y ), x = x ( u, v ), and y = y ( u, v ), suppose that x (2 , 3) = 4 and y (2 , 3) = 5. Find z v (2 , 3) in terms of some of the numbers a, b, c, d, e, r, s, t , where f x (2 , 3) = a, f y (2 , 3) = b, x u (2 , 3) = c, y u (2 , 3) = d, f x (4 , 5) = e, f y (4 , 5) = r, x v (2 , 3) = s, y v (2 , 3) = t. Solution: z v (2 , 4) = es + rt 2. Let f ( x, y ) = cos( x 2 + y 2 ). Find all four second partial derivatives of f ( x, y ), and check that f xy ( x, y ) = f yx ( x, y ). Solution: First
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Unformatted text preview: f x ( x, y ) =-2 x sin( x 2 + y 2 ), so that f xx ( x, y ) =-2 sin( x 2 + y 2 )-4 x 2 cos( x 2 + y 2 ) , f xy ( x, y ) =-4 xy cos( x 2 + y 2 ) . Similarly, f y ( x, y ) =-2 y sin( x 2 + y 2 ), so f yy ( x, y ) =-2 sin( x 2 + y 2 )-4 y 2 cos( x 2 + y 2 ) , f yx ( x, y ) =-4 xy cos( x 2 + y 2 ) ....
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