Math 2433 – 12021, Spring 2017
EMCF 4
Sections 13.4 – 13.5, 14.1 – 14.4
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· Submit the completed assignment at http://www.casa.uh.edu under "EMCF" and
choose EMCF 4.
1. A particle travels one time around the helix X(t) = (cos t, sin t, t) (that is, as t goes from 0 to 2π). What is the distance that the particle has traveled?
a.
b.
c.
d.
e.
f. None of these
2. Which of the following functions is depicted in the contour plot below?
a.
b.
c.
d.
e. None of these
3. Give the domain of
a.
b.
c.
d.
e. None of these
4. Give the range of
a.
b.
c.
d.
e. None of these
5. Give the domain of
a.
b.
c.
d.
e. None of these
6. Give the range of
a.
b.
c.
d.
e. None of these
7. The surfaces intersect in a space curve C. Determine the projection of C onto the xy-plane for the sphere x2+y2+(z − 2)2 = 2 and the cone x2+y2 = z2.
a.
b.
c.
d.
e. None of these
8. Identify the level curves of the given surface.
a. parabolas
b. hyperbolas
c. ellipses
d. exponentials
e. circles
f. none of these
9. Identify the level curves of the given surface.
a. parabolas
b. hyperbolas
c. logarithms
d. ellipses
e. exponentials
f. none of these
10. Find the equation of the level curve for that contains the point P(1,0)
a.
b.
c.
d.
e. None of these
11. Let . Find
a.
b.
c.
d.
e.
f. None of these
12. Let . Find
a.
b.
c.
d.
e.
f. None of these
13. Let . Find
a.
b.
c.
d.
e.
f. None of these
Use the following for problems 14 & 15:
14.
a.
b.
c.
d.
e.
f. None of these
15.
a.
b.
c.
d.
e.
f. None of these
16. If , then
a.
b.
c.
d.
e.
f. None of these
17. Let . Find .
a.
b.
c.
d.
e.
f. None of these