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Stewart_Calc_7ET ch02sec01
MULTIPLE CHOICE
1. A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the
number of heartbeats after t minutes. When the data in the table are graphed, the slope of the
tangent line represents the heart rate in beats per minute. The monitor estimates this value
by calculating the slope of a secant line. Use the data to estimate the patient's heart rate after
42 minutes using the secant line between the points with .
a.
b.
c.
d.
e.
f.
2. The displacement (in feet) of a certain particle moving in a straight line is given by
where t is measured in seconds. Find the average velocity over the interval
Round your answer to three decimal places.
a.
b.
c.
d.
e.
f.
3. If a ball is thrown into the air with a velocity of , its height (in feet) after t seconds is
given by
.
Find the velocity when
a.
b.
c.
d.
e.
4. If a rock is thrown upward on the planet Mars with a velocity of , its height in meters
t seconds later is given by
.
Find the average velocity over the time interval .
a.
b.
c.
d.
e.
5. The point lies on the curve . If is the point Q , use your
calculator to find the slope of the secant line PQ (correct to six decimal places) for the value
a.
b.
c.
d.
e.
6. The position of a car is given by the values in the following table.
(seconds)
0
1
2
3
4
(meters)
0
23.7
27
58.3
90.5
Find the average velocity for the time period beginning when and lasting 2 seconds.
a.
b.
c.
31.75
d.
e.
33.5
NUMERIC RESPONSE
1. The position of a car is given by the values in the following table.
Estimate the instantaneous velocity when by averaging the velocities for the periods
.
2. A tank holds gallons of water, which drains from the bottom of the tank in half an
hour. The values in the table show the volume V of water remaining in the tank (in gallons)
after minutes. If is the point on the graph of V, fill the table with the slopes of
the secant lines where Q is the point on the graph with the corresponding .
Enter your answer to two decimal places.
t
Slope
5
10
20
25
30
