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Mathematical Expression Editor

Please answer this question to the best of your ability. You are welcome to re-watch
parts of any of the videos to help you.

Problems 1 and 2 refer to the following context.

Li is out for a bike ride. He starts his ride from a bike shop. The function expresses
the relationship between Li’s velocity (in meters per minute) as he bikes and the
number of minutes elapsed since he started biking.

What does the product approximate?

The average rate of change of Li’s velocity over a particular interval.The change
in Li’s distance away from the bike shop over a particular interval.Li’s
instantaneous velocity at a particular moment in time.Li’s acceleration over a
particular interval.Li’s distance away from the bike shop after having run for
minutes.

What does the sum approximate?

Li’s distance away from the bike shop after having run for 2.5 minutes.The
average rate of change of Li’s velocity over the interval of time from to .The
change in Li’s distance away from the bike shop over the interval of time from to .Li’s distance away from the bike shop after having run for 3 minutes.Li’s
acceleration over the interval of time from to .

The function expresses the relationship between the rate at which water drains from
a tank (in gallons per minute) and the number of minutes elapsed since water
started draining from the tank. What quantity does the sum of the areas of the blue
rectangles on the graph of the function below approximate?

The average rate at which water drained from the tank over the interval of time
from 2 to 14 minutes after water started draining from the tank.The total amount
of water drained from the tank over the interval of time from 2 to 14 minutes after
water started draining from the tank.The constant rate at which water would have
to drain for the tank to be empty 20 minutes after water started draining.The instantaneous rate at which water drains from the tank 14 minutes
after water started draining.The initial amount of water in the tank.

The function represents the relationship between the rate of change in the value of
investment stocks (in dollars per month) and the number of months elapsed since
the stocks were purchased. Which of the following sums approximates the change in
the value of the stocks over the interval of time from 4 to 7 months after the stocks
were purchased?

The table below shows the horizontal velocity of a baseball (in feet per second) for
various values of , which is the number of seconds elapsed since the baseball was
thrown.

t

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

v(t)

132

130.03

128.08

126.16

124.27

122.41

120.58

118.78

117

Approximate the total distance the ball traveled during the first two seconds after it
was thrown by computing a left-hand Riemann sum with four terms.