Evaluate the surface integral y dA where H is the helicoid (ie., spiral ramp) given by the vector parametric equation H (u, v) = (u cos v, u sinu, v), 0

Q: →> Let S be the surface in R³ that is the image of the function F: R² R³ given by F(u, v) = (u²,…

A: The given surfaces are Fu,v=u2,v2,u+v and 2x2+y2+z2=7. To show that the point 1,1,2 lie on both the…

Q: Sketch and describe, in your own words, the surface S parametrized as follows: r(u, v) = (3 cos v,…

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Q: Evaluate F. dS , where F = and S is the helicoid with vector equation r(u, v) = 0 < u < 1, 0 < v<T…

A: since, y,-x,z3 and, ru,v=u cosv, u sinv,v So, F⇀ru,v=u cosv,-u sinv, v3 Now the normal upward vector…

Q: Calculate Tu, T, and n(u, v) for the parametrized surface at the given point. Then find the equation…

A: In the given question we have to find the Tu , Tv and n(u, v) and tangent plane.

Q: An equation of the tangent plane to the parametrized surface at the point corresponding to u…

A: Given parametrized surface equation is

Q: Use polar coordinates to integrate under z=xy above the first quadrant of the unit circle on the xy…

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Q: Evaluate /| F. d5 , where F = and S is the helicoid with - vector equation r(u, v) = 0 < u < 1, 0…

A: To evaluate the below vector surface integral. ∫∫SF⋅dS

Q: a. Find the normal vector to the tangent plane b. Find an equation of the tangent plane to the given…

A: What is Parametric Surface: The concept of parameterized curves is extended to vector-valued…

Q: Let S be the surface of revolution of the curve C : z? + (y+ 5)² = 4. (a) Find a parametrization of…

A: Consider the curve C in zy-plane as shown: \ On rotating the curve around z-axis, we get The shape…