# Презентация - Mathematical Induction

Смотреть слайды в полном размере  Вашему вниманию предлагается презентация на тему «Mathematical Induction», с которой можно предварительно ознакомиться, просмотреть текст и слайды к ней, а так же, в случае, если она вам подходит - скачать файл для редактирования или печати.

Презентация содержит 20 слайдов и доступна для скачивания в формате ppt. Размер скачиваемого файла: 1.90 MB

Pic.1 Pic.2 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].
Pic.3 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].
Pic.4 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.
Pic.5 Question 1. Using the Principle of Mathematical Induction show that Question 1. Using the Principle of Mathematical Induction show that
Pic.6 Pic.7 Pic.8 Pic.9 Question 1b. Using the Principle of Mathematical Induction show that Question 1b. Using the Principle of Mathematical Induction show that
Pic.10 Pic.11 Question 3a. Calculate the following sum Question 3a. Calculate the following sum
Pic.12 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.
Pic.13 Pic.14 Question 6. Use the Cauchy criterion to show Question 6. Use the Cauchy criterion to show
Pic.15 Pic.16 Picture of the Week
Pic.17 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
Pic.18 b) Is it possible that there exists a number a such that b) Is it possible that there exists a number a such that
Pic.19 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
Pic.20 Если вам понравился сайт и размещенные на нем материалы, пожалуйста, не забывайте поделиться этой страничкой в социальных сетях и с друзьями! Спасибо!                  