# P3 - lim x a f ( x ) = r or lim x a f ( x ) =-r . That is,...

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Math 141, Problem Set #3 (due in class Fri., 9/23/11) Stewart, section 1.3, problems 24, 32, 34, 44, 46. (Note: For problem 1.3.24, you don’t need to ﬁnd ALL δ ’s that work, or even the largest δ that works; it’s enough to ﬁnd ONE δ that works, so just ﬁnd one that’s easy to compute with!) Note that for Problem 46, you must appeal directly to Deﬁnition 4 (and not, say, Theorem 3). Stewart, section 1.4, problems 2, 8, 12, 16, 24, 30, 32, 34, 44. Also: A. Prove that | ab | = | a || b | . B. Consider the function f ( x ) = ( 1 if x is rational - 1 if x is irrational . (a) What is lim x 0 f ( x )? (b) What is lim x 0 xf ( x )? C. Prove or disprove the proposition “If lim x a [ f ( x )] 2 = r 2 , then either
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Unformatted text preview: lim x a f ( x ) = r or lim x a f ( x ) =-r . That is, decide whether you believe this proposition is true for every proposition f or there are exceptions, and then justify your belief with either a deduction (if the proposition is true) or a counterexample (if the proposition is false). D. Prove lim x x 2 sin 1 /x = 0. Please dont forget to write down on your assignment who you worked on the assignment with (if nobody, then write I worked alone), and write down on your time-sheet how many minutes you spent on each problem (this doesnt need to be exact)....
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## This note was uploaded on 02/13/2012 for the course MATH 141 taught by Professor Staff during the Fall '11 term at UMass Lowell.

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