Taxicab fares. In New York City, taxicabs change passengers $2.50 for entering a cab and then $050 for each one-fifth of a mile (or fraction thereof) traveled. (There are additional charge for slow traffic and idle times, but these are not considered in this problem.) If x presents the distance traveled in miles, then C ( x ) is the cost of the taxi fare, where C ( x ) = $ 2.50 , if x = 0 , C ( x ) = $ 3.00 , if 0 < x ≤ 0.2 , C ( x ) = $ 3.50 , if 0.2 < x ≤ 0.4 , C ( x ) = $ 4.00 , if 0.4 < x ≤ 0.6 , and so on. The graph of C is show below. (Source; New York City Taxi and Limousine Commission.) Using the graph of the taxicab fare function, find each of the following limits. if it exists. lim x → 0.25 − C ( x ) , lim x → 0.25 + C ( x ) , lim x → 0.25 C ( x )
Taxicab fares. In New York City, taxicabs change passengers $2.50 for entering a cab and then $050 for each one-fifth of a mile (or fraction thereof) traveled. (There are additional charge for slow traffic and idle times, but these are not considered in this problem.) If x presents the distance traveled in miles, then C ( x ) is the cost of the taxi fare, where C ( x ) = $ 2.50 , if x = 0 , C ( x ) = $ 3.00 , if 0 < x ≤ 0.2 , C ( x ) = $ 3.50 , if 0.2 < x ≤ 0.4 , C ( x ) = $ 4.00 , if 0.4 < x ≤ 0.6 , and so on. The graph of C is show below. (Source; New York City Taxi and Limousine Commission.) Using the graph of the taxicab fare function, find each of the following limits. if it exists. lim x → 0.25 − C ( x ) , lim x → 0.25 + C ( x ) , lim x → 0.25 C ( x )
Solution Summary: The author explains that taxicabs charge passengers 2.50 for entering a cab, and ifx=0 C(x)=3.
Taxicab fares. In New York City, taxicabs change passengers $2.50 for entering a cab and then $050 for each one-fifth of a mile (or fraction thereof) traveled. (There are additional charge for slow traffic and idle times, but these are not considered in this problem.) If x presents the distance traveled in miles, then
C
(
x
)
is the cost of the taxi fare, where
C
(
x
)
=
$
2.50
,
if
x
=
0
,
C
(
x
)
=
$
3.00
,
if
0
<
x
≤
0.2
,
C
(
x
)
=
$
3.50
,
if
0.2
<
x
≤
0.4
,
C
(
x
)
=
$
4.00
,
if
0.4
<
x
≤
0.6
,
and so on. The graph of C is show below. (Source; New York City Taxi and Limousine Commission.)
Using the graph of the taxicab fare function, find each of the following limits. if it exists.
lim
x
→
0.25
−
C
(
x
)
,
lim
x
→
0.25
+
C
(
x
)
,
lim
x
→
0.25
C
(
x
)
Let m(t) be a continuous function with a domain of all real numbers. The table below shows some of the values of m(t) .
Assume the characteristics of this function are represented in the table.
t
-3 -2 8 11
12
m(t) -7 6
3
-9
0
(a) The point (-3, -7) is on the graph of m(t). Find the corresponding point on the graph of the transformation y = -m(t) + 17.
(b) The point (8, 3) is on the graph of m(t). Find the corresponding point on the graph of the transformation y =
-m (−t) .
24
(c) Find f(12), if we know that f(t) = |m (t − 1)|
f(12) =
Suppose the number of people who register to attend the Tucson Festival of Books can be modeled by P(t) = k(1.1),
where t is the number of days since the registration window opened. Assume k is a positive constant.
Which of the following represents how long it will take in days for the number of people who register to double?
t =
In(1.1)
In(2)
In(2)
t =
In(1.1)
In(1.1)
t =
t =
t =
In(2) - In(k)
In(2)
In(k) + In(1.1)
In(2) - In(k)
In(1.1)
Use the method of washers to find the volume of the solid that is obtained
when the region between the graphs f(x) = √√2 and g(x) = secx over the
interval ≤x≤ is rotated about the x-axis.
Chapter 1 Solutions
Calculus and Its Applications, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)
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