Exam 1 Review
1. Use the graph
given in the above figure to find the following values, if they exist. If a limit does
not exist, explain why.
a.
b.
e.
f.
c.
g.
d.
h.
i.
2. Complete the table and use the result to estimate the limit.
3. In the following function find an open interval about
Then give a value for
holds.
such that for all satisfying
a.
b.
c.
4. Use the
a.
definition to prove the following.
b.
5. Find the limit if it exists.
a.
b.
c.
d.
g.
j.
m.
e.
h.
f.
i.
k.
n.
l.
on which the inequality
the inequality
holds.
6. Suppose
and
a.
Find
b.
c.
d.
7. Let
Compute the following limits or state that they do not exist.
a.
b.
c.
8.
Let the above graph be represented by the function
a. Find
b. Does
and
exist? If so, what is it? If not, why not?
c. Find
and
d. Does
exist? If so, what is it? If not, why not?
9. Find the limits
a.
b.
c.
d.
e.
f.
g.
h.
10. For what values of is
continuous at every
11. Find the limits.
a.
d.
b.
c.
e.
f.
Solution:
1. a. 3
b. 2
c. 3
d. Does not exist e. 2
f. 3
g. 2
h. 3
2.
Based on the above table we can estimate the limit as 4.
3.
a.
b.
c.
5.
a.
b.
c.
i.
j.
k.
d.
l.
6.
a.
7.
a.
8.
a.
b. No,
c.
d. Yes,
a.
b.
9.
b.
b.
c.
e.
f.
m.
n.
g.
d.
c. Does not exist.
c.
d. 1
e.
d.
e.
f.
10.
11.
a.
h.
b.
c.
f.
g.
h.
i. 3