c3-t3(1)

∂ z ∂ v(b assume that f x y z = 0 defines z

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Unformatted text preview: ∂ z ∂ v (b) Assume that F ( x , y , z ) = 0 defines z implicitly as a function of x and y . Show that if ∂ F / ∂ z ≠ 0, then ∂ z ∂ y ∂ F / ∂ y ∂ F / ∂ z . ______________________________________________________________________ 6. (10 pts.) Locate all relative extrema and saddle points of the following function. f ( x , y ) x 4 y 4 4 xy Use the second partials test in making your classification. (Fill in the table below after you locate all the critical points.) Crit.Pt. f xx @ c.p. f yy @ c.p. f xy @ c.p. D @ c.p. Conclusion TEST3/MAC2313 Page 4 of 5 ______________________________________________________________________ 7. (10 pts.) (a) Evaluate the following iterated integral. ⌡ ⌠ ln(3) ⌡ ⌠ ln(2) e x y dydx (b) Very carefully write down, but do not evaluate , an iterated integral whose numerical value is the volume under the plane z = 2 x + y and over the rectangle R = {(x,y) : 3 ≤ x ≤ 5, 1 ≤ y ≤ 2}. V ______________________________________________________________________ 8. (10 pts.) Evaluate the integral below by first reversing the order of integration.Evaluate the integral below by first reversing the order of integration....
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∂ z ∂ v(b Assume that F x y z = 0 defines z implicitly...

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