Consider x = h(y,z) as a parametrized surface in the
natural way. Write the equation of the tangent plane to the surface at
the point (2, 2, 2) given that and .
.

x-2+4(y-2)-5(z-2) = 0

The work

2.

For the surface with parametric equations
r(s,t) = &lang st, s + t, s - t &rang,
find the equation of the tangent plane at (2,3,1).
.

Find the surface area under the restriction

Equation of tangent plane: -2(x-2)+3(y-3)-(z-1)=0

surface area: 7.013

The work

3.

Find the surface area of that part of the plane
2x + 10y + z = 10 that lies inside the elliptic cylinder
Surface Area =

643.83

The work

4.

Write down the iterated integral which expresses the surface area of
over the triangle with vertices
(-1,1), (1,1), (0,2):

a =
b =
f(y) =
g(y) =
h(x,y) =

a = 1
b = 2
f(y) = y-2
g(y) = 2-y
h(x,y) =

The work

5.

The vector equation r(u,v) = ucos(v)i + usin(v)j + vk , 0 &le v &le 8&pi, 0 &le u &le 1, describes a helicoid (spiral
ramp). What is the surface area?

28.85

The work

6.

Find the surface area of the part of the sphere
that lies above the cone

7.36

The work

7.

Find the area cut out of the cylinder by the cylinder
.

8

The work

8.

If a parametric surface given by
and
-4 &le u &le 4, -5 &le v &le 5, has surface area equal to 5,
what is the surface area of the parametric surface given by
with
-4 &le u &le 4, -5 &le v &le 5?