1. The graph of is given below. Based on this graph determine where the
function is discontinuous.
2. The graph of is given below. Based on this graph determine where the
function is discontinuous.
3. The graph of is given below. Based on this graph determine where the
function is discontinuous.
For problems 4 13 using only Properties 1- 9 from the Limit Properties
section, one-sided limit properties (if needed) and the definition of
continuity determine if the given function is continuous or discontinuous at
the indicated points.
4.
(a) ,
(b) ,
(c) ?
5.
(a)
,
(b) ,
(c) ?
6.
(a)
, (b)
, (c)
?
7.
(a)
, (b)
, (c)
?
8.
(a)
,
(b) ?
9.
(a)
,
(b) ?
10.
(a)
,
(b) ?
11.
(a)
,
(b) ?
12.
(a)
,
(b) ?
13.
(a)
,
(b) ?
For problems 14 22 determine where the given function is
discontinuous.
14.
15.
16.
17.
18.
19.
20.
21.
22.
For problems 23 27 use the Intermediate Value Theorem to show
that the given equation has at least one solution in the indicated interval. Note that you are NOT asked to find the solution
only show that at least one must exist in the indicated interval.
23. on
24. on
25. on
26.
on
27. on
For problems 28 33 assume that is continuous everywhere unless otherwise
indicated in some way. From the given
information is it possible to determine if there is a root of in the given interval?
If it is possible to determine that there is a root in the given
interval clearly explain how you know that a root must exist. If it is not possible to determine if there
is a root in the interval sketch a graph of two functions each of which meets
the given information and one will have a root in the given interval and the
other will not have a root in the given interval.
28. and on the interval .
29. and on the interval .
30. and on the interval .
31. ,
,
,
and on the interval .
32. ,
,
,
and on the interval .
33. ,
,
,
and on the interval
.