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Math 3012 MathematicsMath 3012 MathematicsMath 3012 Mathematics
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w. h′(w) = Solution: SOLUTION Recall that
w = w^1 /^2 , so that
h′(w) = (− 2 ) · (− 3 )w−^3 −^1 +
w−^1 /^2 = 6 w−^4 + 7 w−^1 /^2.
Correct Answers:
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 + 52 = − 2 .5. Similarly, the y-coordinate of the center equals − 2 + 52 = 0 .5, and the z-coordinate of the center equals 2 − 52 = − 0 .5. Correct Answers:
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]
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:
(b) z = 2 − x^2 − y^2
-?
(c) z = 2
-?
(d) z = 2 + x − 2 y 1
(e) z = 2 − x + 2 y
-?
(f) z = 2 − x
-?
Solution: SOLUTION (a) z = 2 + x^2 + y^2 is an upward opening parabaloid with pos- itive z intercept, centered on the z-axis, and so is none of these graphs. (b) z = 2 − x^2 − y^2 is a downward opening parabaloid with pos- itive z intercept, centered on the z-axis, and so is 3. (c) z = 2 is a plane parallel to the x- and y-axes, with positive z intercept., and so is 1. (d) z = 2 + x − 2 y is a plane with positive y and z intercepts, and negative x intercept, and so is none of these graphs. (e) z = 2 − x + 2 y is a plane with positive x and z intercepts, and negative y intercept, and so is 2. (f) z = 2 − x is a plane parallel to the y-axis, with positive x and z intercepts., and so is 4. Correct Answers:
Solution: SOLUTION Let’s look at what each of the graphs tells us:
Generated by c©WeBWorK, http://webwork.maa.org, Mathematical Association of America
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