Need help with part c). Please explain each step and neatly type up. Thank you :) 8. Let S be a parametric surface(a)(b)(c)r(u, v) = (u cos v, u sin v, v); u = [0, 2], v = [0, π].(*) Find ru, and rv.(**) Calculate ru x rv.to S?icos v-u sin v= sin vi- cos vj + ukru x rv = detjsin vu cos v(**) What is the total charge on the surface S if the surface chargedensity is given by restricting the functiono(x, y, z) ==k01x² + y²

Surface integral of a function f(x,y,z) on a parametric surface r(u,v) in the region D ∫∫Dfx(u,v) ,…

(a) (b) (c) r(u, v) = (u cos v, u sin v, v); u € [0, 2], v € [0, π]. (*) Find r, and r. (**) Calculate ru x rv. to S? i Cos v -u sin v = sin vi- cos vj + uk ru xrv = det j sin v u cos v k 0 1, (**) What is the total charge on the surface S if the surface charge density is given by restricting the function o(x, y, z)=√x² + y²

(a) (b) (c) r(u, v) = (u cos v, u sin v, v); u € [0, 2], v € [0, π]. (*) Find r, and r. () Calculate ru x rv. to S? i Cos v -u sin v = sin vi- cos vj + uk ru xrv = det j sin v u cos v k 0 1, () What is the total charge on the surface S if the surface charge density is given by restricting the function o(x, y, z)=√x² + y²

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.6: Parametric Equations

Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...

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