The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower and upper estimates for the distance that she traveled during these three seconds. t(s) (8) 0.5 1.0 1.5 2.0 2.5 3.0
v(ft/s) 0 6.2 10.8 14.9 18.1 19.4 20.2
Step 1
We will use either L or Rg for the upper and lower estimates. Since the runner's speed is an increasing function, then (No Response) will give the lower estimate, and (No Response) will give the upper estimate.
Step 2
The sub-interval widths At for this situation are At = (No Response)
Step 3
The first two sub-intervals in the table are [0, 0.5] and [0.5, 1.0). When calculating L6, we should use the function values v = (No Response) and v- (No Response) for these two sub-intervals, respectively.
Step 4
Enter your answers from smallest to largest. In the last step, round your answer to one decimal place. For the lower estimate, we have the following.
L6 - (0.5)(0+ 6.2 + (No Response) (No Response) + (No Response) + (No Response))
Step 5
Enter your answers from smallest to largest. In the last step, round your answer to one decimal place. For the upper estimate, we have the following.
R6 = (0.5) (No Response) + (No Response) + (No Response) + (No Response) + (No Response) + (No Response))