Презентация - Mathematical Induction

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Презентация Mathematical Induction


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Mathematical Induction, слайд 1
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Question 0. A continuous function f is defined on the interval [−1,1], and f 2(x) = x 2 for each x f
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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Question 0+. A function f is defined on the interval [−1,1], and f 2(x) = x 2 for each x from the in
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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Mathematical Induction Let Sn, n = 1,2,3,… be statements involving positive integer numbers n. Suppo
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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Question 1. Using the Principle of Mathematical Induction show that Question 1. Using the Principle
Question 1. Using the Principle of Mathematical Induction show that Question 1. Using the Principle of Mathematical Induction show that
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Mathematical Induction, слайд 6
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Mathematical Induction, слайд 7
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Mathematical Induction, слайд 8
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Question 1b. Using the Principle of Mathematical Induction show that Question 1b. Using the Principl
Question 1b. Using the Principle of Mathematical Induction show that Question 1b. Using the Principle of Mathematical Induction show that
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Mathematical Induction, слайд 10
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Question 3a. Calculate the following sum Question 3a. Calculate the following sum
Question 3a. Calculate the following sum Question 3a. Calculate the following sum
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Question 5. Using the formula for the derivative of inverse function derive explicit formulae for th
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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Mathematical Induction, слайд 13
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Question 6. Use the Cauchy criterion to show Question 6. Use the Cauchy criterion to show
Question 6. Use the Cauchy criterion to show Question 6. Use the Cauchy criterion to show
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Mathematical Induction, слайд 15
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Picture of the Week
Picture of the Week
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Question 4. Let f (x) be a differentiable function such that the derivative is a continuous function
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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b) Is it possible that there exists a number a such that b) Is it possible that there exists a numbe
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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c) Let x1 be a solution of the equation f (x) = x. Find c) Let x1 be a solution of the equation f (x
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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Mathematical Induction, слайд 20


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