Project 9
MAC 2233
1. Consider the following piecewise defined function for various choices of constants
p
and
q
.
Sketch its graph in the case that
p
=
q
= 1
.
f
(
x
) =

p
x
x <

1
2
x
=

1
2

x

1
< x <
2
√
x
+
q
x
≥
2
Determine whether
f
(
x
)
is continuous at
x
=

1
,
x
= 0
, and
x
= 2
. Classify each discontinu
ity as infinite, jump, or removable.
jump discontinuities at
x
=

1
,
2
continuous at
x
= 0
2. For what choices of
p
and
q
do the limits
lim
x
→
1
f
(
x
)
and
lim
x
→
2
f
(
x
)
both exist?
Do these
choices make
f
(
x
)
continuous? Why or why not? Sketch the graph of
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 Spring '08
 Smith
 Calculus, Continuous function, various choices

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