Содержание
- 2. Irrational Numbers
- 3. Question 1. The Dirichlet function is defined Is this function even or odd or neither? Is
- 4. The sum of two rational numbers is a rational The sum of a rational and an
- 5. Therefore f (x + y) = f (x) for any rational number y. Thus, the Dirichlet
- 6. Question 2. The numbers and are irrational. Show that the number is irrational too. Solution. We
- 7. Contradiction!!! is a rational number. Therefore our assumption was incorrect and is an irrational number.
- 8. Question 3. Let and denote Find a general formula for the second derivative of inverse function,
- 9. Since f (0) = 0, we have g (0) = 0.
- 10. Question. Which of the following conditions imply that a real number x is rational? I. is
- 11. a) I only b) II only c) I and II only d) I and III only
- 12. Calculus++ Also known as Hysterical Calculus
- 13. Question 1. Show that is irrational. Solution. Any integer number n is either even, n =
- 14. Let us now assume that is a rational That is, k2 is even, and hence k
- 15. Thus, our assumption that is a rational number leads to a contradiction, and hence this number
- 16. Higher derivatives Notations for n-th order derivatives: The following properties are often useful for calculating high-order
- 17. Question 5. Find the n-th derivative of the function Solution. Recall the formula for the sum
- 18. Therefore
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