Larson_Calculus_10e ch01sec04
MULTIPLE CHOICE
1. Use the graph as shown to determine the following limits, and discuss the continuity of the function at
.
(i) (ii) (iii)
a.
b.
2 , 2 , 2 ,
c.
d.
2 , 2 , 2 ,
e.
2. Use the graph as shown to determine the following limits, and discuss the continuity of the function at
.
(i) (ii) (iii)
a.
b.
c.
d.
e.
3. Use the graph to determine the following limits, and discuss the continuity of the function at .
(i) (ii) (iii)
a.
b.
c.
d.
e.
4. Find the limit (if it exists).
a.
b.
c.
d.
e.
5. Find the limit (if it exists).
a.
b.
c.
d.
e.
6. Find the limit (if it exists).
a.
b.
c.
d.
e.
7. Find the limit (if it exists). Note that represents the greatest integer function.
a.
b.
c.
d.
e.
8. Find the limit (if it exists). Note that represents the greatest integer function.
a.
b.
c.
d.
e.
9. Discuss the continuity of the function .
a.
b.
c.
d.
e.
10. Find the x-values (if any) at which the function is not continuous. Which of
the discontinuities are removable?
a.
b.
c.
d.
e.
11. Find the x-values (if any) at which is not continuous.
a.
b.
c.
d.
e.
12. Find the x-values (if any) at which the function is not continuous. Which of the
discontinuities are removable?
a.
10 and – , removable
b.
discontinuous everywhere
c.
continuous everywhere
d.
10 and – , not removable
e.
0, removable
13. Find the x-values (if any) at which the function is not continuous. Which of the
discontinuities are removable?
a.
b.
c.
d.
e.
14. Find the x-values (if any) at which is not continuous.
a.
b.
c.
d.
e.
15. Find the constant a such that the function
is continuous on the entire real line.
a.
1
b.
c.
d.
e.
16. Find the constants a and b such that the function
is continuous on the entire real line.
a.
b.
c.
d.
e.
17. Find the value of c guaranteed by the Intermediate Value Theorem.
a.
b.
c.
d.
e.
18. Find the value of c guaranteed by the Intermediate Value Theorem.
a.
b.
c.
d.
e.
19. A long distance phone service charges $ for the first minutes and $ for each additional
minute or fraction thereof. Use the greatest integer function to write the cost C of a call in terms of
time t (in minutes).
a.
b.
c.
d.
e.
20. Find all values of c such that is continuous on .
a.
b.
c.
d.
e.