hw2 - 1 If f x< g x for all x then lim x → a f x< lim...

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University of Engineering and Technology Lahore Department of Electrical Engineering Calculus I Problem Set #2 Due date: November 16, 2010 Announcements Quiz 1 next week! Irfan’s office hours: Thursday 9:30-11:30. Also feel free to walk in any other time when you need help. Reading Section 2.1-2.4, section A.2 (pages AP-6 and AP-7 only) of textbook. Chapter 5 from Spivak (at the photocopier). 1. Exercise 2.3. Questions 9, 10, 11, 17, 21, 25, 57, 58 2. Exercise 2.4. Questions 2, 6 3. (a) Suppose that f ( x ) g ( x ) for all x . Prove that lim x a f ( x ) lim x a g ( x ), provided that these limits exist. (b) Prove or disprove
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Unformatted text preview: 1 : If f ( x ) < g ( x ) for all x , then lim x → a f ( x ) < lim x → a g ( x ). 4. Prove or disprove: If lim x → a f ( x ) and lim x → a g ( x ) do not exist, then neither lim x → a ( f + g )( x ) exists nor the lim x → a ( fg )( x ) exists. 5. Give an example where lim x → a f ( x 2 ) exists but lim x → a f ( x ) does not. 6. Prove that lim x → a f ( x ) exists if lim x → a + f ( x ) = lim x → a-f ( x ) 1 Disproving is in general easier than proving: you just have to come up with one example in which the statement is false 1...
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