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Stewart_Calc_7ET ch16sec06
MULTIPLE CHOICE
1. Match the equation with one of the graphs below.
a.
c.
b.
d.
2. Find the area of the surface.
The part of the plane ; ,
a.
b.
c.
d.
3. Find the area of the surface.
The part of the paraboloid ; ,
a.
b.
c.
d.
4. Find the area of the part of the cone that is cut off by the cylinder
a.
b.
c.
d.
5. Find the area of the surface.
The part of the paraboloid ; ,
a.
58
51
2 11
b.
c.
d.
6. Find a parametric representation for the part of the elliptic paraboloid that
lies in front of the plane x = 0.
a.
b.
c.
d.
e.
7. Find the area of the part of the surface that lies between the planes x = 0, x = 4,
, and z = 1.
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. Find a parametric representation for the part of the plane that lies inside the cylinder
2. Set up, but do not evaluate, a double integral for the area of the surface with parametric
equations
3. Find a parametric representation for the part of the sphere that lies above
the cone
4. Find the area of the part of paraboloid that lies inside the cylinder
SHORT ANSWER
1. Find the area of the surface S where S is the part of the plane that lies above the
triangular region with vertices , and
2. Find the area of the surface S where S is the part of the surface that lies inside the
cylinder
3. Find the area of the surface S where S is the part of the sphere that lies to
the right of the xz-plane and inside the cylinder
4. Find the area of the surface S where S is the part of the sphere that lies
inside the cylinder
5. Find an equation in rectangular coordinates, and then identify the surface.
6. Find an equation in rectangular coordinates, and then identify the surface.
7. Find a vector representation for the surface.
The plane that passes through the point and contains the vectors and
..
8. Find an equation of the tangent plane to the parametric surface represented by r at the
specified point.
;
9. Find an equation of the tangent plane to the parametric surface represented by r at the
specified point.
; u = ln 5, v = 0
10. Find an equation of the tangent plane to the parametric surface represented by r at the
specified point.
; u = ln 9, v = 0
11. Use the Divergence Theorem to find the flux of F across S; that is, calculate .
; S is the sphere
