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MATH 231 / Spring 2008
February 20, 2008
Name:
Key
1. (3 points) Match the following functions with their graphs.
(a)
z
= sin(
xy
)
(b)
z
= sin(
x

y
)
(c)
z
= sin
x

sin
y
(1)
(2)
(3)
Solution:
(a)
=
(1)
,
(b)
=
(2)
,
(c)
=
(3)
.
2. (7 points) Find the limit, if it exists, or show that the limit does not exist.
lim
(
x,y,z
)
→
(0
,
0
,
0)
x
2
+ 2
y
2
+ 3
z
2
x
2
+
y
2
+
z
2
Solution:
We will prove that this limit does not exist. To do so, we will look at the limit of the function as it
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Unformatted text preview: approaches (0 , , 0) along the following paths: 1: x = x, y = 0 , z = 0 and 2: x = 0 , y = y, z = 0. 1: Setting y = z = 0, We have lim x → x 2 x 2 = lim x → 1 = 1 2: Let’s set x = z = 0. Then we get lim y → 2 y 2 y 2 = lim y → 2 = 2 Since these two values are not equal, the limit does not exist. 1...
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This homework help was uploaded on 04/17/2008 for the course MATH 231 taught by Professor Bociu during the Spring '08 term at UVA.
 Spring '08
 BOCIU
 Math, Calculus

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