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Stewart_Calc_7ET ch14sec02
MULTIPLE CHOICE
1. Evaluate the limit.
a.
0
b.
c.
d.
e.
2. Use a table of numerical values of f (x, y) for (x, y) near the origin to make a conjecture
about the value of the limit of f (x, y) as .
a.
b.
c.
1
d.
e.
the value cannot be determined
3. Evaluate the limit.
a.
the limit does not exist
b.
c.
2
d.
0
e.
1
4. Determine the largest set on which the function is continuous.
a.
b.
c.
d.
e.
5. Find the limit
a.
34
b.
80
c.
260
d.
16
6. Find the limit
a.
b.
c.
d.
1
5
−1
5
1
−1
7. Find the limit
a.
b.
c.
d.
8. Find the limit Hint: If and then
if and only if
a.
b.
c.
d.
9. Determine where the function is continuous.
a.
b.
c.
1
6
0
29
14
−1
6
9
7
1
0
7
9
d.
10. Find the limit
a.
b.
c.
d.
NUMERIC RESPONSE
1. Find , if and .
2. Find the limit.
3. Determine the largest set on which the function is continuous.
13
9
0
−1
6
1
6
4. Find the limit.
5. Use polar coordinates to find the limit.
6. Use spherical coordinates to find the limit.
SHORT ANSWER
1. Determine where the function is continuous.
2. Determine where the function is continuous.
3. Consider evaluating the limit
(a) Evaluate the limit along the path
(b) Evaluate the limit along the path
(c) What can you conclude about the existence of ?
4. Find and determine where h is continuous.
