3. [-/8 Points] DETAILS SCALCET9 5.1.009.MI.SA. This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise 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) 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 first sketch an approximate graph of the velocity function of the runner using the given table. We then shade the region whose area represents the total distance the runner travels in the first three seconds. Doing so gives the following result t (s) 0 .5 1.0 1.5 2.0 2.5 3.0 (ft/s) 0 6.2 10.8 14.9 18.1 19.4 20.2 25 20 15 LO 0.5 1.0 1.5 2.0 2.5 3.0 We will approximate the area of the shaded region using the method of approximationg rectangles. Recall that this can be done using either the left endpoints or the right endpoints of the subintervals. One will give an estimate that is smaller than the actual value, and the other will give an estimate that is larger than the actual value. In the given table we note that there are six clear subintervals: [0, 0.5], [0.5, 1.0], [1.0, 1.5], [1.5, 2.0], [2.0, 2.5], and [2.5, 3.0]. The width of each of these subintervals is . Therefore, the change in t over each subinterval, At, can be stated as follows. At =