265Lesson09Problems(1)

265Lesson09Problems(1) - p 1 . 02 + 1 . 99 3 and compare...

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MATH 265: MULTIVARIABLE CALCULUS: LESSON 9 PROBLEMS Problems are worth 20 points each. (1) Let f ( x,y ) = sin xy + x cos y . Compute f x ( x,y ) ,f y ( x,y ), and f xy ( x,y ). (2) Let f ( x,y,z ) = x + ln(2 y + 3 z 2 ). Compute ∂f ∂x , 2 f ∂y∂x , and 3 f ∂z∂y∂x . Evaluate 2 f ∂y∂x (2 , 1 , - 2). (3) Compute ∂α ± α 2 + β 2 1 + e αβ ² . (4) Find an equation for the plane tangent to the surface given by z = x 2 + y 4 + e xy at the point (1 , 0 , 2). (5) Use a (logically chosen) linear approximation of f ( x,y ) = p x + y 3 to estimate p 1 . 02 + 1 . 99 3 . Use a calculator to compute
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Unformatted text preview: p 1 . 02 + 1 . 99 3 and compare the result to the approximation. (The approximation better be pretty close to the calculator value!) (6) (Bonus question: worth 10 points. Total points for assignment not to exceed 100.) Find the x,y , and z intercepts of the plane tangent to the sphere of radius 14, with center at the origin, at the point (1 , 2 , 3). 1...
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