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Exercise 2. Prove that if f: ER and g: ER are uniformly continuous, then so is f(x) + g(x). Exercise 3. Prove that if f: ER and g: ER are uniformly continuous and bounded, then f(x)g(x) is uniformly continuous. Exercise 4. State precisely the following definitions:

Exercise 2. Prove that if f: ER and g: ER are uniformly continuous, then so is f(x) + g(x). Exercise 3. Prove that if f: ER and g: ER are uniformly continuous and bounded, then f(x)g(x) is uniformly continuous. Exercise 4. State precisely the following definitions:

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.3: Factorization In F [x]
Problem 23E: Let f(x),g(x),h(x)F[x] where f(x) and g(x) are relatively prime. If h(x)f(x), prove that h(x) and...
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Exercise 2. Prove that if f: ER and g: ER are uniformly continuous, then so is f(x) + g(x). Exercise 3. Prove that if f: ER and g: ER are uniformly continuous and bounded, then f(x)g(x) is uniformly continuous. Exercise 4. State precisely the following definitions:
Transcribed Image Text:Exercise 2. Prove that if f: ER and g: ER are uniformly continuous, then so is f(x) + g(x). Exercise 3. Prove that if f: ER and g: ER are uniformly continuous and bounded, then f(x)g(x) is uniformly continuous. Exercise 4. State precisely the following definitions:
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