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hw3 - | f | is continuous everywhere 3 Find a function that...

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University of Engineering and Technology Lahore Department of Electrical Engineering Calculus I Problem Set #3 Due date: November 30 , 2010 Announcements Quiz 1 this week on Thursday at 12:10 p.m. Section A in E-3, Section B in E-3A, Section C in Electronics Lab, Section D in Basic EE Lab. It will cover Problem Sets 1 and 2. New Office hours: Come in the break time to see me. Reading Section 2.6 of Thomas’ Calculus Chapters 6 and 7 from Spivak at the photocopier 1 1. Thomas’ Calculus Exercise 2.6. Questions 1, 2, 5, 29, 35, 39, 51, 52. 2. Give an example of a function f such that f is continuous nowhere but
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Unformatted text preview: | f | is continuous everywhere. 3. Find a function that is discontinous at 1 , 1 2 , 1 3 , 1 4 , ··· but continuous at all other points. 4. Find a function that is discontinous at 1 , 1 2 , 1 3 , 1 4 , ··· and a at 0, but continuous at all other points. 5. Prove that if f is continous at a then | f | is also continous at a . 6. Suppose that f satisfies f ( x + y ) = f ( x ) + f ( y ) and f is continous at 0. Prove that f is continous at a for all a . 1 suggestion: Do not spend too much time reading the proofs of Theorems 9, 10 and 11 in Chapter 7. 1...
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