Mathematics: A Discrete Introduction - 3 Edition - Chapter 10 - Problem 10.2
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# For each of the following sets, find a way to rewrite the set using set-builder notation

Mathematics: A Discrete Introduction | 3rd Edition

Problem 10.2

For each of the following sets, find a way to rewrite the set using set-builder notation (rather than listing the elements). a. f1; 2; 3; 4; 5; 6; 7; 8; 9; 10g. b. f8; 6; 4; 2; 0; 2; 4; 6; 8g. c. f1; 3; 5; 7; 9; 11; 13; : : :g. d. f1; 4; 9; 16; 25; 36; 64; 81; 100g.

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MATH152 | Amy Austin | Week 1 Section 5.5 | Integration by Substitution • U-Substitution – Unwinding the Chain Rule • The Substitution Rule [in math terms, and then more simply explained]: o If u=g(x) is a differentiable function, then ∫ f(g(x))g’(x)dx = ∫ f(u)du o ∫ f(g(x))g’(x)dx ▪ u = g(x); where u is the differentiable expression ▪ du = g’(x)dx; where du is the derivative of ‘u’ ▪ Substitute ‘u’ and ‘du’ into the given integral to get ∫ f(u)du • Steps to Integrate using U-Substitution 1. Examine the integral a. Look for an expression and its derivative if possible b.

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