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The statement The square of any rational number is

Discrete Mathematics: Introduction to Mathematical Reasoning | 1st Edition | ISBN: 9780495826170 | Authors: Susanna S. Epp ISBN: 9780495826170 210

Solution for problem 3.30 Chapter 3

Discrete Mathematics: Introduction to Mathematical Reasoning | 1st Edition

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Discrete Mathematics: Introduction to Mathematical Reasoning | 1st Edition | ISBN: 9780495826170 | Authors: Susanna S. Epp

Discrete Mathematics: Introduction to Mathematical Reasoning | 1st Edition

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Problem 3.30

The statement The square of any rational number is rational can be rewritten formally as For all rational numbers x, x2 is rational or as For all x, ifx is rational then x2 is rational. Rewrite each of the following statements in the two forms x, and x, if , then or in the two forms x and y, and x and y, if , then .a. The reciprocal of any nonzero fraction is a fraction. b. The derivative of any polynomial function is a polynomial function. c. The sum of the angles of any triangle is 180. d. The negative of any irrational number is irrational. e. The sum of any two even integers is even. f. The product of any two fractions is a fraction.

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Chain Rule We need to find derivatives of compositions of 2 or more functions. Ex. f(x) = sin(x^2), g(x)= x + 1, h(x)= cos(sintan(x)) The chain rule F(x)=f(g(x)), F’(x)=f’(g(x))*g’(x) Ex. F(x) = sin(x^2) the other function f(g(x)) is sin(g(x)) the inner function g(x) is x^2 F’(x) = cos(x^2)*d/dx x^2,cos(x^2)*2x Ex. g(x) = x + 1, d/dx( x + 1) = d/dx (x^2+1)^½ The outer function is the power of ½, the inner function is x^2 +1 d/dx [ x^2 +1)^½] = ½(x^2+1)^-½* d/dx(x^2+1) = ½(X^2+1)^-½*2x ​this answer is perfectly acceptable Ex. d/dx [(x^4+x)^10] = 10(x^4+x)^9 * 4x^3 +1 Ex. d/dx (sin^8(x)) Remember sin^n(x) = (sin(x))^n So d/dx [(sin(x))^8] =8(sin(x))^7 * cos(x) Mini Formula = d/dx ((f(x)^n) = n/f(x))^n-1 * f’(x) Advice always rewrite trig functions like the equation above

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Chapter 3, Problem 3.30 is Solved
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Textbook: Discrete Mathematics: Introduction to Mathematical Reasoning
Edition: 1
Author: Susanna S. Epp
ISBN: 9780495826170

Discrete Mathematics: Introduction to Mathematical Reasoning was written by and is associated to the ISBN: 9780495826170. This full solution covers the following key subjects: . This expansive textbook survival guide covers 10 chapters, and 2065 solutions. Since the solution to 3.30 from 3 chapter was answered, more than 420 students have viewed the full step-by-step answer. The answer to “The statement The square of any rational number is rational can be rewritten formally as For all rational numbers x, x2 is rational or as For all x, ifx is rational then x2 is rational. Rewrite each of the following statements in the two forms x, and x, if , then or in the two forms x and y, and x and y, if , then .a. The reciprocal of any nonzero fraction is a fraction. b. The derivative of any polynomial function is a polynomial function. c. The sum of the angles of any triangle is 180. d. The negative of any irrational number is irrational. e. The sum of any two even integers is even. f. The product of any two fractions is a fraction.” is broken down into a number of easy to follow steps, and 127 words. The full step-by-step solution to problem: 3.30 from chapter: 3 was answered by , our top Math solution expert on 01/04/18, 08:37PM. This textbook survival guide was created for the textbook: Discrete Mathematics: Introduction to Mathematical Reasoning, edition: 1.

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The statement The square of any rational number is