homework 4-solutions - everts (cce382) homework 4 luecke...

everts (cce382) – homework 4 – luecke – (55550) 1
This print-out should have 15 questions.
Multiple-choice questions may continue on
the next column or page – find all choices
before answering.
001 10.0points
Find the domain of the function
f ( x,y ) = ln(7 - x
2
- 5 y
2
) .
1.
braceleftBig
( x, y ) :
1
7
x
2
+
5
7
y
2
≤ 1
bracerightBig
x
x
x x
x
x
x x
Determine the volume, V , of the box as a
function of x and y .
( x, y ) :
1
x
2
+
5
y
2
< 1
bracerightBig
.
7 7
keywords: function several variables, ln func-
tion, domain
002 10.0points
A rectangular piece of cardboard is 3 times
as long as it is wide. If the length of the
shorter side is y inches and an open box is
constructed by cutting equal squares of side-
length x inches from the corners of the piece of
cardboard and turning up the sides as shown
in the figure
V ( x ) = (length) × (width) × (height)
= x (3 y - 2 x )( y - 2 x ) .
Consequently,
V ( x ) = 3 xy
2
- 8 x
2
y + 4 x
3
cu. ins .
003 10.0points
Which one of the following functions has

everts (cce382) – homework 4 – luecke – (55550) 2
-2
-1
0
1
2
x
-2
-1
0
1
2
y
0
2
4
6
8
z
-2
-1
0
1
2
x
-2
-1
0
1
2
0
2
4
6
8
as its graph.
1. f ( x,y ) =
1
2
(8 - x
2
- y
2
)
2. f ( x,y ) = 2 x
2
3. f ( x,y ) =
1
2
( x
2
+ y
2
)
4. f ( x,y ) = y
2
- x
2
5. f ( x,y ) = 2 y
2
correct
Explanation:
The cross-section of the graph by the plane
y = 0 gives a straight line parallel to the x - y
plane, indicating that the function does not