Larson_Calculus_10e ch01sec05
MULTIPLE CHOICE
1. Determine whether approaches or as x approaches from the left and from
the right by completing the tables below.
–3.1
–3.01
–3.001
–2.999
–2.99
–2.9
–2.5
a.
b.
c.
d.
2. Find all the vertical asymptotes (if any) of the graph of the function
a.
b.
c.
d.
e.
no vertical asymptotes
3. Find the vertical asymptotes (if any) of the function .
a.
b.
c.
d.
e.
4. Find all the vertical asymptotes (if any) of the graph of the function .
a.
b.
c.
d.
e.
5. Find all the vertical asymptotes (if any) of the graph of the function .
a.
b.
c.
d.
e.
6. Find all vertical asymptotes (if any) of the function .
a.
b.
c.
d.
e.
7. Find the vertical asymptotes (if any) of the function .
a.
b.
c.
d.
e.
8. Find the limit.
a.
b.
c.
d.
e.
9. Find the limit.
a.
b.
c.
d.
e.
10. Find the limit.
a.
b.
c.
d.
e.
11. Find the limit (if it exists).
a.
b.
c.
d.
e.
12. Use a graphing utility to graph the function and determine the one-sided limit
.
a.
b.
c.
0
d.
e.
8
13. Use a graphing utility to graph the function and determine the following one-sided
limit.
a.
b.
c.
d.
e.
14. A -foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from
the house at a rate of 2 feet per second, the top will move down the wall at a rate of
, where x is the distance between the base of the ladder and the house. Find the
rate r when x is feet.
a.
ft/sec
b.
ft/sec
c.
d.
ft/sec
e.
ft/sec
15. A 25-foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from
the house at a rate of 2 feet per second, the top will move down the wall at a rate of
where x is the distance between the base of the ladder and the house. Find the
limit of r as .
3
2
4
3
2
3
3
4
a.
b.
c.
d.
e.