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# Let Un) be a sequence of functions that converges uniformly to I on A and that ISBN: 9780471321484 424

## Solution for problem 24 Chapter 8.1

Introduction to Real Analysis | 3rd Edition

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Problem 24

Let Un) be a sequence of functions that converges uniformly to I on A and that satisfiesIIn(x) I ~ M for alln E N and all x EA. If g is continuous on the interval [- M, M], show thatthe sequence (g 0 In) converges uniformly to g 0 I on A.

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CH 1010: General Chemistry Dr. Ava Kreider-Mueller FINAL EXAM CHAPTER 1: Key Terms-  Steps of the Scientific Method: 1. Ask a Question 2. Background Research on the topic 3. Create a Hypothesis 4. Test your Hypothesis 5. Analyze your data, and draw a conclusion 6. Report all findings, check if hypothesis was correct  Hypothesis: a testable explanation  Scientific Theory: a explanation which has been repeated tested  Scientific Law: a statement of a fundamental principle that can be applied to a topic.  Meter: distance traveled by light emitted from a helium-neon laser through a vacuum  Matter: anything that has a mass and occupies space o 3 States of Matter are: 1. Solid 2. Liquid 3. Gas  Weight: measure of force that gravity exerts on an object. Weight can change since gravity can change but mass stays the same  Mass: quantity of matter in an object 3 Most Common Units of Temperature: 1. Fahrenheit, Fº 2. Celsius, Cº 3. Kelvin, Kº [Both Celsius and Kelvin have the same temperature interval] If you are finding Kº use the following equation: Kº = Temp. in Cº + 273.15 If you are finding Cº use the following equation: Cº = Temp. in Kº - 273.15

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