hw8 - 1 f Use the Sequential Criterion for limits to prove...

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MATH 444: ELEMENTARY REAL ANALYSIS HOMEWORK 8 Due date: Oct 22 (Wed) Exercises from the textbook. 4.1: 3; 6; 9(b)(d); 11; 12(b)(d); 17 4.2: 5 Out-of-textbook exercises. 1. For each of the following sets find the set of its cluster points. (a) A = ( - 1 , 0 ] ( 1 , 2 ) { 3 } { 4 } { 6 n 2 n + 1 n N } . (b) A = ( 0 , 1 ) Q . 2. Let D R and f D R . What is the largest possible domain for
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Unformatted text preview: 1 f ? Use the Sequential Criterion for limits to prove that lim x → a f ( x ) = L ≠ ±⇒ lim x → a 1 f ( x ) = 1 L . Caution : Whenever you divide by anything, make sure it is not 0. 3. Prove Theorem 4.2.7 of the textbook....
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