11. Find the equation of the tangent plane to the surface xyz + z²/3 = y² at (−1,1,1). 12. Use Green's Theorem to evaluate f xydx + x²dy on the path described by the boundary of the graphs y = x², y = √x oriented counterclockwise. 13. Evaluate the surface integral f f f (x, y, z)ds for f(x, y, z) = x²z², S: on the cone z² = x²+ y², between the planes z = 1, z=3. [Hint: converting to cylindrical/polar will help.]

11. Find the equation of the tangent plane to the surface xyz + z²/3 = y² at (−1,1,1). 12. Use Green's Theorem to evaluate f xydx + x²dy on the path described by the boundary of the graphs y = x², y = √x oriented counterclockwise. 13. Evaluate the surface integral f f f (x, y, z)ds for f(x, y, z) = x²z², S: on the cone z² = x²+ y², between the planes z = 1, z=3. [Hint: converting to cylindrical/polar will help.]

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 34E

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