Question 1. Let S be the surface consisting in the part of the cone x² + y² = between the planes z = 2 and z = 4. Evaluate the surface integral of over S. w = zdy Adz + (y+z)dx / dy

Q: 5. Find a parametric representation for the part of the sphere x + y + z2 = 4 that lies between the…

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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: Use Stokes' theorem to evaluate ∮C z2 ex^2 dx +xy2 dy + tan−1 (y) dz where C is the circle x2 + y2 =…

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Q: How do you calculate the area of a parametrized surface in space? Of an implicitly defined surface…

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Q: Find the points on the surface y² = 16 + xz that are closest to the origin. smaller y-value (x, y,…

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Q: 3. Show that the improper integral x*e*dx is convergent and gives the answer of 4! (It turns out…

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Q: Graph the solid that lies between the surface z= 2xy/( x2 + 1) and the plane z =x + 2y and is…

A: Given surfaces are z=2xyx2+1, z=x+2y  and are bounded by planes x=0 , x=2 , x=-1 , y=0 , y=4. To…

Q: 4. Consider the surface defined by the portion of the cone z = -Vx2 + y? that lies below the…

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Q: 1) Let S be the surface of the cylinder r+y = 4 with y >0 and -15z<1. Find a parametric equation…

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Q: parametrization of the surface z = 3x² + 8x, ymbolic notation and fractions where needed.

A: In this question, the concept of the tangent plane is applied. The equation of the tangent plane of…

Q: Give a parameterization for the surface z F(u, v) = (u, v, ). x² - y²: = x

A: NOTE: Refresh your page if you can't see any equations. . the given surface is

Q: Find all points where the surface z = xy e-* + 2y-) has a horizontal tangent plane. %3D O A. O B.…

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Q: Consider the surface given by x2 + y? + z? = a². Show that every normal line to this surface passes…

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Q: Let f(x,y,z)=-x^2+sin(y)-2z^2=0 define a surface in 3 dimensions. Find the equation of the normal…

A: Given the surface fx,y,z=-x2+siny-2z2=0. Let us find the equation of the normal to the surface in…

Q: . Use Stokes' Theorem (and only Stokes' Theorem) to evaluate F dr, where F(r,y,z) = (3y, -2x, 3y)…

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Q: Evaluate f(V x F) dS where S is the surface x² + y² +3z² = 1, z ≤0 and F = (y, -x, zx³y²). Let the…

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