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
)
The position of a moving hockey puck after t seconds is s(t) = tan
a. Find the velocity of the hockey puck at any time t.
v(t)
=====
b. Find the acceleration of the puck at any time t.
-1
a (t)
=
(t) where s is in meters.
c. Evaluate v(t) and a (t) for t = 1, 4, and 5 seconds. Round to 4 decimal places, if necessary.
v (1)
v (4)
v (5)
a (1)
=
=
=
=
a (4) =
a (5) =
d. What conclusion can be drawn from the results in the previous part?
○ The hockey puck is decelerating/slowing down at 1, 4, and 5 seconds
○ The hockey puck has a constant velocity/speed at 1, 4, and 5 seconds
○ The hockey puck is accelerating/speeding up at 1, 4, and 5 seconds
question 8
Find the area of the surface obtained by rotating the circle x² + y² = r² about the line y = r.
Chapter 1 Solutions
Calculus and Its Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Bittinger, Ellenbogen & Surgent, The Calculus and Its Applications Series)
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