Title: Riemann Sums Introduction PostVideo Questions
Course: Calculus I

Q: The table below shows the horizontal velocity v(t) of a baseball (in feet per second) for various values of t, 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.
- 126.2325 (Incorrect)
- 250 (Incorrect)
- 250.5775 (Incorrect)
- 250.58 (Incorrect)
- 250.6 (Incorrect)
- 252 (Incorrect)
- 252.465 (Correct)
- 279.8275 (Incorrect)
A: 252.465

Q: The function y = g(t)represents the relationship between the rate of change in the value of investment stocks (in dollars per month) and the number of months t elapsed since the stocks were purchased. Which of the following sums approximates the change in value of the stocks over the interval of time from 4 to 7 months after the stocks were purchased?
- [Image: equation] (Incorrect)
- [Image: equation] (Incorrect)
- [Image: equation] (Incorrect)
- [Image: equation] (Incorrect)
- [Image: equation] (Correct)
A: [Image: equation]

Q: The function y = r(t) expresses the relationship between the rate at which water drains from a tank (in gallons per minute) and the number of minutes t 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 y = r(t) below approximate?
[Image: PIC]
- 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. (Incorrect)
- The total amount of water drained from the tank over the interval of time from 2 to 14 minutes after water water started draining from the tank. (Correct)
- The constant rate at which water would have to drain for the tank to be empty 20 minutes after water started draining. (Incorrect)
- The instantaneous rate at which water drains from the tank 14 minutes after water started draining. (Incorrect)
- The initial amount of water in the tank. (Incorrect)
A: The total amount of water drained from the tank over the interval of time from 2 to 14 minutes after water water started draining from the tank.

Q: Li is out for a bike ride. He starts his ride from a bike shop. The function y = v(t) expresses the relationship between Li's velocity (in meters per minute) as he bikes and the number of minutes t elapsed since he started biking.
What does the sum [Image: equation] approximate?
- Li's distance away from the bike shop after having biked for 2.5 minutes (Incorrect)
- The average rate of change of Li's velocity over the interval of time from t = 0 to t =(5)/(2) . (Incorrect)
- The change in Li's distance away from the bike shop over the interval of time from t=0 to t=3. (Correct)
- Li's distance away from the bike shop after having biked for 3 minutes (Incorrect)
- Li's acceleration over the interval of time from t=0 to t=6. (Incorrect)
A: The change in Li's distance away from the bike shop over the interval of time from t=0 to t=3.

Q: Li is out for a bike ride. He starts his ride from a bike shop. The function y = v(t) expresses the relationship between Li's velocity (in meters per minute) as he bikes and the number of minutes t elapsed since he started biking.
What does the product [Image: equation] approximate?
- The average rate of change of Li's velocity over a particular [Image: equation] interval. (Incorrect)
- The change in Li's distance away from the bike shop over a particular [Image: equation] interval. (Correct)
- Li's instantaneous velocity at a particular moment in time. (Incorrect)
- Li's acceleration over a particular [Image: equation] interval. (Incorrect)
- Li's distance away from the bike shop after having biked for t minutes. (Incorrect)
A: The change in Li's distance away from the bike shop over a particular [Image: equation] interval.