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Chapter 2 | Limits
22. [T] Compute the average velocity of the runner over the given time intervals. a. ⎡ ⎣ 1.95, 2.05 ⎤ ⎦
b. ⎡ c. ⎡
⎣ 1.995, 2.005 ⎤ ⎦ ⎣ 1.9995, 2.0005 ⎤ ⎦
d. [2, 2.00001]
23. Use the preceding exercise to guess the instantaneous velocity of the runner at t =2 sec. For the following exercises, consider the function f ( x ) = | x |. 24. Sketch the graph of f over the interval [−1, 2] and shade the region above the x -axis. 25. Use the preceding exercise to find the aproximate value of the area between the x -axis and the graph of f over the interval [−1, 2] using rectangles. For the rectangles, use the square units, and approximate both above and below the lines. Use geometry to find the exact answer. For the following exercises, consider the function f ( x ) = 1− x 2 . ( Hint : This is the upper half of a circle of radius 1 positioned at (0, 0).) 26. Sketch the graph of f over the interval [−1, 1]. 27. Use the preceding exercise to find the aproximate area between the x -axis and the graph of f over the interval [−1, 1] using rectangles. For the rectangles, use squares 0.4 by 0.4 units, and approximate both above and below the lines. Use geometry to find the exact answer. For the following exercises, consider the function f ( x ) =− x 2 +1. 28. Sketch the graph of f over the interval [−1, 1]. 29. Approximate the area of the region between the x -axis and the graph of f over the interval [−1, 1].
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