Chapter 3 - Continuous Functions and Limits

# Chapter 3 - Continuous Functions and Limits - Chapter 3...

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Chapter 3 – Continuous Functions and Limits Section 3.1 – Continuity Pg 43, Definition – A function is said to be continuous at the point x o in D provided that whenever is a sequence in D that converges to x o , the image sequence converges to f(x o ). The function is said to be continuous at every point in D. Pg 44, Theorem 3.1 – Suppose that the functions and are continuous at the point x o in D. Then the sum the product and, if for all x in D, the quotient Pg 45, Corollary 3.2 – Let be a polynomial. Then is continuous. Moreover, if is also a polynomial and , then the quotient is continuous. Pg 45, Definition – For functions and such that f(D) is contained in U, we define the composition of with , denoted by , by the formula Pg 45, Theorem 3.3 – For functions and such that f(D) is contained in U, suppose that is continuous at the point x o in D and is continuous at the point f(x o ). Then the composition is continuous at x o . Section 3.2 – The Extreme Value Theorem

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Chapter 3 - Continuous Functions and Limits - Chapter 3...

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