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MIDTERM2 20C

# MIDTERM2 20C - Find the critical points of the following...

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1 MIDTERM II NAME MATH 20C (please print) TA’S NAME (please print) FORM B Problem 1. (12 pts.) Compute partial derivatives ∂f ∂y , 2 f ∂x∂y , 2 f ∂y 2 of the following function: f ( x,y ) = sin ( x 2 + y 2 ) Problem 2. (14 pts.) Use the linear approximation to estimate the given value: 2 ð 3 . 98 2 + 3 . 05 2

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2 Problem 3. (12 pts.) Let f ( x,y,z ) = x - 1 ye y + z and let r ( t ) = ( t,e t , 1+ t ) . Compute the derivative d dt ( f ( r ( t )) . Problem 4. (14 pts.) Let f ( x,y,z ) = x 2 y cos ( y + z ) and let x = u - v,y = uv,z = 2 u + v. Let F ( u,v ) = f ( x ( u,v ) ,y ( u,v ) ,z ( u,v )) . Compute the partial derivatives: ∂F ∂u and ∂F ∂v .
3 Problem 5. (16 pts. )

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Unformatted text preview: Find the critical points of the following function and determine if they are local minima or maxima. f ( x,y ) = x 3 + 2 xy-2 y 2-10 x-2 Problem 6. (16 pts) Let f ( x,y ) = yx. Find the minimum and maximum of the function f subject to the constrain x 2 + y 2 = 8 . 4 Problem 7. (16 pts) Compute the following integral: Ú Ú D 3 e x 3 dA where D is the region: 0 ± y ± x 2 , ± x ± 1 ....
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MIDTERM2 20C - Find the critical points of the following...

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