Question

Find the area of the surface. The part of the paraboloid z=1-x^2-y^2 that lies above the plane z=-2

(Please post hand writing one) thank you

Answer #1

Find the area of the surface
The part of the parabloid z=4-x^2-y^2 that lies above the
xy-plane

Consider the part of the paraboloid x = 4 − y ^2 − z ^2 that
lies in front of the plane x = 0.
(a) What is its mass if its density is ρ(x, y, z) = y^2 + z ^2
g/cm^2 ?
(b) What is its surface area?

Find the volume of the solid that lies under the paraboloid z =
x^2 + y^2 , above the xy-plane and inside the cylinder x^2 + y^2 =
1.

Consider the surface given by the part of the plane z=y+3 that
lies inside the cylinder x^2+y^2=4
a. Find a parametric representation of the surface
b. find the area of the above surface

7. What is the surface area of the paraboloid parametrized in
problem 5(b)?
(The paraboloid from problem 5(b) is z = 4 - x^2 - y^2 which
lies above the xy-plane)

In the following problems, the surface S is the part of the
paraboloid z= x^2 + y^2 which lies below the plane z= 4, and
includes the circular intersection with this plane. This single
surface S could also be described as being contained inside the
cylinder x^2+y^2= 4.
(a) Iterate, but do not evaluate, the integral ∫∫S(z+x) dS in
terms of two parameters. Write the integrand in simplest form.
(b) Use Stoke’s theorem to rewrite ∫S(delta X F) · ndS...

find volume lies below surface
z=2x+y and above the region in xy plane bounded by x=0 ,y=1
and x=y^1/2

Let F(x, y, z) = z tan−1(y^2)i + z^3 ln(x^2 + 7)j + zk. Find the
flux of F across S, the part of the paraboloid x^2 + y^2 + z = 29
that lies above the plane z = 4 and is oriented upward.

Let F(x,y,z) = ztan-1(y^2) i + (z^3)ln(x^2 + 8) j + z k. Find
the flux of F across the part of the paraboloid x2 + y2 + z = 20
that lies above the plane z = 4 and is oriented upward.

Use surface integrals to find the area of the part of the
surface given z = x2 + y that lies above the triangle with
verticies (0, 0), (1, 0), and (1, 2).

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