2.
4/4 points |
Previous Answers
SCalcET7 2.5.009.
The toll
T
charged for driving on a certain stretch of a toll road is
$2
except during rush hours (between 7 AM and 10 AM and between 4 PM
and 7 PM) when the toll is
$4
.
(a) Sketch a graph of
T
as a function of the time
t
, measured in hours past midnight.
continuous from the right
continuous from the left
neither
continuous from the right
continuous from the left
neither

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hw05S2.5-6
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(b) Locate the discontinuities of
T
. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
Classify the discontinuities as removable, jump, or infinite.
Discuss the significance of the discontinuities of
T
to someone who uses the road.

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hw05S2.5-6
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(b) The function
T
has jump discontinuities at
Their significance to someone who uses the road is that, because of the
sudden jumps in the toll, they may want to avoid the higher rates between
and
and between
and
if feasible.
t
= 7, 10, 16, and 19.
t
= 7
t
= 10
t
= 16
t
= 19

12/14/16, 4(14 PM
hw05S2.5-6
3.
5/5 points |
Previous Answers
SCalcET7 2.5.013.
Use the definition of continuity and the properties of limits to show that the function is continuous at the given number
a
.
1.
−
1
2
f
(
x
) =
x
+
2
x
5 3
=
x
+
2
x
5
= [
−
1 +
2
(
−
1)
5
]
3
=
−
27
=
f
(
−
→
−
1
lim
x
→
−
1
a
=
−
1.
1).
lim
x

Page 5 of 19
4.
5/5 points |
Previous Answers
SCalcET7 2.5.019.
Consider the following.
(
x
) =
,
a
=
x
if
x
<
x
2
if
x
≥
Find the left-hand and right-hand limits at the given value of
a
.
f
(
x
) =
,
a
=
x
if
x
<
x
2
if
x
≥
1
e
1
1

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