AP Calculus Slides October 29, 2007
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Workshop on the definite integral and the Fundamental Theorem of Calculus part 1.
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AP Calculus Slides October 29, 2007
- 2. Let for 0 ≤ x ≤ 1. (a) Using n = 4 subintervals, Find L(4) and U(4), lower and upper estimates for (b) Find the difference between the upper and lower estimates, U(4) - L(4). (c) Represent U(4) - L(4) geometrically on a graph of ƒ. (d) How large would n need to be to be sure that U(n) - L(n) ≤ 0.005?
- 3. Let for 0 ≤ x ≤ 1. (a) Using n = 4 subintervals, Find L(4) and U(4), lower and upper estimates for (b) Find the difference between the upper and lower estimates, U(4) - L(4). (c) Represent U(4) - L(4) geometrically on a graph of ƒ. (d) How large would n need to be to be sure that U(n) - L(n) ≤ 0.005?
- 4. The table below gives values of a continuous function g at several inputs x. Estimate using a midpoint sum with three equal subintervals. Then draw a sketch that illustrates this sum geometrically.
- 5. Real cars don't adhere to explicit speed formulas. What can be observed, practically speaking, are numerical speed data, like those below. (Notice the irregular time intervals; real data often have gaps.) How far did the car travel in one hour? Find the best approximation you can.
- 6. Real cars don't adhere to explicit speed formulas. What can be observed, practically speaking, are numerical speed data, like those below. (Notice the irregular time intervals; real data often have gaps.) How far did the car travel in one hour? Find the best approximation you can.