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20 слайдов
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1,2,3,4,5,6,7,8,9,10,11
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Слайды и текст к этой презентации:
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Содержание слайда: Question 0. A continuous function f is defined on the interval [−1,1], and f 2(x) = x 2 for each x from the interval [−1,1].
Question 0. A continuous function f is defined on the interval [−1,1], and f 2(x) = x 2 for each x from the interval [−1,1].
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Содержание слайда: Question 0+. A function f is defined on the interval [−1,1], and f 2(x) = x 2 for each x from the interval [−1,1].
Question 0+. A function f is defined on the interval [−1,1], and f 2(x) = x 2 for each x from the interval [−1,1].
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Содержание слайда: Mathematical Induction
Let Sn, n = 1,2,3,… be statements involving positive integer numbers n.
Suppose that
1. S1 is true.
2. If Sk is true, then Sk +1 is also true.
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Содержание слайда: Question 1. Using the Principle of Mathematical Induction show that
Question 1. Using the Principle of Mathematical Induction show that
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Содержание слайда: Question 1b. Using the Principle of Mathematical Induction show that
Question 1b. Using the Principle of Mathematical Induction show that
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Содержание слайда: Question 3a. Calculate the following sum
Question 3a. Calculate the following sum
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Содержание слайда: Question 5. Using the formula for the derivative of inverse function derive explicit formulae for the derivatives of arcsin x, arccos x, arctan x, and arccot x.
Question 5. Using the formula for the derivative of inverse function derive explicit formulae for the derivatives of arcsin x, arccos x, arctan x, and arccot x.
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Содержание слайда: Question 6. Use the Cauchy criterion to show
Question 6. Use the Cauchy criterion to show
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Содержание слайда: Picture of the Week
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Содержание слайда: Question 4. Let f (x) be a differentiable function such that the derivative is a continuous function and f (f (x)) = x for any x. Furthermore, let f (0) = 1, and f (1) = 0.
Question 4. Let f (x) be a differentiable function such that the derivative is a continuous function and f (f (x)) = x for any x. Furthermore, let f (0) = 1, and f (1) = 0.
a) Is it possible that there exists a number a such that
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Содержание слайда: b) Is it possible that there exists a number a such that
b) Is it possible that there exists a number a such that
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Содержание слайда: c) Let x1 be a solution of the equation f (x) = x. Find
c) Let x1 be a solution of the equation f (x) = x. Find
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