Evaluate the surface integral ∫∫_S F*ndA by the divergence theorem. Show the details. F=[e^x, e^y, e^z], S the surface of the cube |x|≤1, |y|≤1, |z|≤1

How to calculate leaf surface area?

Evaluate the surface integral. ∫∫sz dS, where S is the part of the paraboloid

$$z = x^2 + y^2$$

that lies under the plane z = 4

Evaluate the surface integral.

$$∫∫s (x^2z + y^2z)dS,$$

where S is the part of the plane

$$z = 4 + x + y$$

that lies inside the cylinder

$$x^2+y^2=4$$

Evaluate the surface integral ∫∫_S F*ndA by the divergence theorem. Show the details. F=[x², y², z²], S the surface of the cone x²+y²≤z², 0≤z≤h

Find the coordinates of all points on the surface with equation $z=x^{4}-4 x y^{3}+6 y^{2}-2$ where the surface has a horizontal tangent plane.

Classify and sketch the quadric surface. z² = x² + y²/9

Sketch the surface given by the function.

$$f(x, y)=y^2$$

Evaluate the surface integral through S (x+y+z) dS, S is the parallelogram with parametric equations x=u+v, y=u-v, z=1+2u+v, 0<=u<=2, 0<=v<=1

Describe and sketch the surface. \

$$y^2+z=4$$

The surface area $A$ of a cube with side $s$ is given by

$$A=6s^2.$$

If a cube's surface area is $54 \mathrm{~in}^2$, find the volume of the cube.

Find the surface area of the given surface. The torus $\langle(c+a \cos v) \cos u,(c+a \cos v) \sin u, a \sin v\rangle$, c>a>0

Express the area of the given surface as an iterated double integral, and then find the surface area. The portion of the plane 2x+2y+z=8 in the first octant.

Evaluate the surface integral.

$\iint_S z d S$, $S$ is the surface $x=y+2 z^2, 0 \leqslant y \leqslant 1,0 \leqslant z \leqslant 1$