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Worksheet_6_PrelimIIPrep

# Worksheet_6_PrelimIIPrep - the skill level as follows 1 2 2...

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Worksheet 6: Prelim II Review 1) Estimate how much the value of yz x y z y x f 2 sin ) , , ( + = will change if point P(x,y,z) moves 0.1 unit from P 0 (0,1,0) straight toward P 1 (2,2,-2). What is an isosurface? Pick an isosurface for f(x,y,z) above and determine the tangent plane to the isosurface at pt P 1 . 2) Find the linearization of g(x,y,z,w) at the input pt P(1,0,1,1). z w e yz x w z y x g y 2 2 ) , , , ( + + = 3) What is Fubini’s theorem? 4) Draw the region of integration and evaluate: [ ] ∫ ∫ - - - - + + + 1 1 1 1 2 2 2 2 ) 1 ln( y y dy dx xy y x 5) You are an engineer at a manufacturing plant making rubber duckies. The cost of making rubber duckies is ) ( ) , , ( s p l s p l C + = where l is labor time, p is cost of parts, and

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Worksheet 6: Prelim II Review s is the skill level of the workers. Due to a union agreement the labor is constrained by
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Unformatted text preview: the skill level as follows: 1 2 2 = + s l . Due to a supplier contract and just in time manufacturing philosophy at your company the parts and labor are inversely related 1 = lp . Assuming you have complete control over labor, parts, and skill level of employees, minimize the cost of making rubber duckies. 6) Setup the integral in rectangular, cylindrical, and spherical coordinates for the integral of y z y x f 4 6 ) , , ( + = over the region in the first octant bounded by the cone 2 2 y x z + = , the cylinder 1 2 2 = + y x , and the coordinate planes. 7) Determine the flux F = 2 2 , y x across the closed path r = &amp;lt; ) sin( 4 ), cos( t t where 2 t ....
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