Yilin Wang MTH212 Fall2016
Assignment 01 Intro 12.1 12.2 due 09/19/2016 at 11:59pm EDT
1. (1 point) Find the derivative of h(w) = −2w−3+14√w.
h0(w) =
Solution:
SOLUTION
Recall that √w=w1/2, so that
h0(w) = (−2)·(−3)w−3−1+14
2w−1/2=6w−4+7w−1/2.
Correct Answers:
•2*3*wˆ[-1*(3+1)]+14/2*wˆ(-1/2)
2. (1 point) A cube is located such that its top four cor-
ners have the coordinates (−5,−2,2),(−5,3,2),(0,−2,2)and
(0,3,2). Give the coordinates of the center of the cube.
center =
Solution:
SOLUTION
By drawing the top four corners, we find that the length of
the edge of the cube is 5. See the figure below.
We also notice that the edges of the cube are parallel to the
coordinate axis. So the x-coordinate of the the center equals
−5+5
2=−2.5. Similarly, the y-coordinate of the center equals
−2+5
2=0.5, and the z-coordinate of the center equals 2 −5
2=
−0.5.
Correct Answers:
•(-2.5,0.5,-0.5)
3. (1 point) On a separate page, sketch a graph of the equa-
tion x=−1 in 3-space.
Suppose you are observing the coordinate system as shown
below.
If your graph represents a solid (opaque) wall, can you see the
point (1,−3,3)? [?/yes/no]
Which of the following is your graph (note that by clicking
on any graph you will get a larger image)?
graph [?/1/2/3/4/5/6]
1. 2. 3. 4. 5. 6.
Solution:
SOLUTION
The graph is a plane parallel to the yz-plane, and passing
through the point . Accordingly, it looks like graph 1, and if
this is a solid wall, we can see the point (1,−3,3).
Correct Answers:
•yes
•1
4. (1 point) Without a calculator or computer, match the
functions with their graphs in the figures below. Note that two
of the functions do not have a matching graph.
(a) z=2+x2+y2
•?
•1
•2
•3
•4
•none of these graphs
(b) z=2−x2−y2
•?
•1
•2
•3
•4
•none of these graphs
(c) z=2
•?
•1
•2
•3
•4
•none of these graphs
(d) z=2+x−2y
1
