🗊Презентация The Taylor Formula

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The Taylor Formula, слайд №1The Taylor Formula, слайд №2The Taylor Formula, слайд №3The Taylor Formula, слайд №4The Taylor Formula, слайд №5The Taylor Formula, слайд №6The Taylor Formula, слайд №7The Taylor Formula, слайд №8The Taylor Formula, слайд №9The Taylor Formula, слайд №10The Taylor Formula, слайд №11The Taylor Formula, слайд №12The Taylor Formula, слайд №13The Taylor Formula, слайд №14The Taylor Formula, слайд №15The Taylor Formula, слайд №16The Taylor Formula, слайд №17The Taylor Formula, слайд №18The Taylor Formula, слайд №19The Taylor Formula, слайд №20The Taylor Formula, слайд №21The Taylor Formula, слайд №22The Taylor Formula, слайд №23The Taylor Formula, слайд №24The Taylor Formula, слайд №25The Taylor Formula, слайд №26The Taylor Formula, слайд №27The Taylor Formula, слайд №28
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The Taylor Formula, слайд №1
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The Taylor Formula
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The Taylor Formula

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Question 1. If Question 1. If
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Question 1. If Question 1. If

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The Taylor Formula, слайд №4
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The Taylor Formula, слайд №5
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Question 1. What is the greatest value of b for which any function f that satisfies the properties (i), (ii), and (iii) must also satisfy f (1) < 5? Question 1. What is the greatest value of b for which any function f that satisfies the properties (i), (ii), and (iii) must also satisfy f (1) < 5? (i) f (x) is infinitely differentiable for all x; (ii) f (0) = 1, and (iii) for all
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Question 1. What is the greatest value of b for which any function f that satisfies the properties (i), (ii), and (iii) must also satisfy f (1) < 5? Question 1. What is the greatest value of b for which any function f that satisfies the properties (i), (ii), and (iii) must also satisfy f (1) < 5? (i) f (x) is infinitely differentiable for all x; (ii) f (0) = 1, and (iii) for all

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Question 2. Use the Taylor formula to show that e is irrational. Question 2. Use the Taylor formula to show that e is irrational.
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Question 2. Use the Taylor formula to show that e is irrational. Question 2. Use the Taylor formula to show that e is irrational.

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The Taylor Formula, слайд №11
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Question 3. Find Question 3. Find
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Question 3. Find Question 3. Find

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The Taylor Formula, слайд №13
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The Taylor Formula, слайд №14
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The Taylor Formula, слайд №15
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Example. The geometric series Example. The geometric series
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Example. The geometric series Example. The geometric series

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The Taylor Formula, слайд №17
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Question 5. Which of the following series converge? Question 5. Which of the following series converge?
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Question 5. Which of the following series converge? Question 5. Which of the following series converge?

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The Taylor Formula, слайд №21
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Question 5. A certain ball has the property that each time it falls from a height h onto a hard, level surface, it rebounds to a height rh, where 0 < r < 1. Question 5. A certain ball has the property that each time it falls from a height h onto a hard, level surface, it rebounds to a height rh, where 0 < r < 1. Suppose that the ball is dropped from an initial height of H meters. a) Assuming that the ball continues to bounce indefinitely, find the total distance that it travels.
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Question 5. A certain ball has the property that each time it falls from a height h onto a hard, level surface, it rebounds to a height rh, where 0 < r < 1. Question 5. A certain ball has the property that each time it falls from a height h onto a hard, level surface, it rebounds to a height rh, where 0 < r < 1. Suppose that the ball is dropped from an initial height of H meters. a) Assuming that the ball continues to bounce indefinitely, find the total distance that it travels.

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A bouncing ball – total distance travelled A bouncing ball – total distance travelled
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A bouncing ball – total distance travelled A bouncing ball – total distance travelled

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Question 7. A certain ball has the property that each time it falls from a height h onto a hard, level surface, it rebounds to a height r h, where 0 < r < 1. Question 7. A certain ball has the property that each time it falls from a height h onto a hard, level surface, it rebounds to a height r h, where 0 < r < 1. Suppose that the ball is dropped from an initial height of H meters. b) Calculate the total time that the ball spends bouncing. Hint: A ball having zero velocity falls ½ gt2 meters in t seconds.
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Question 7. A certain ball has the property that each time it falls from a height h onto a hard, level surface, it rebounds to a height r h, where 0 < r < 1. Question 7. A certain ball has the property that each time it falls from a height h onto a hard, level surface, it rebounds to a height r h, where 0 < r < 1. Suppose that the ball is dropped from an initial height of H meters. b) Calculate the total time that the ball spends bouncing. Hint: A ball having zero velocity falls ½ gt2 meters in t seconds.

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A bouncing ball – total bouncing time A bouncing ball – total bouncing time
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A bouncing ball – total bouncing time A bouncing ball – total bouncing time

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Question 7. c) Suppose that each time the ball strikes the surface with velocity v, it rebounds with velocity – kv, where 0 < k < 1. Question 7. c) Suppose that each time the ball strikes the surface with velocity v, it rebounds with velocity – kv, where 0 < k < 1. How long will it take for the ball to come to rest?
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Question 7. c) Suppose that each time the ball strikes the surface with velocity v, it rebounds with velocity – kv, where 0 < k < 1. Question 7. c) Suppose that each time the ball strikes the surface with velocity v, it rebounds with velocity – kv, where 0 < k < 1. How long will it take for the ball to come to rest?

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The Taylor Formula, слайд №28
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