math201. quiz_1 - American University of Beirut MATH 201...

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American University of BeirutMATH 201Calculus and Analytic Geometry IIISpring 2005quiz # 1 (very) short answersName:KOBEISSIID #:0001.(10 points, 5 points each)Find each of the following limits:a)limn+n1/nsin(3n2+ 1)
2.(40 points, 10 points each)Determine if the followingseriesconverges or diverges.Justifyyour answersa)+Xn=12nen+ lnnconverges by DCT with+Xn=02enb)+Xn=1(-1)n2nn+e-ndiverges by nth term test
3.(15 points)Find2 - 1/3e1/34. a)(18 points)Find the interval of convergence of the power series+Xn=23n(x+ 1)nn2+ 1
b)(2 points)For what value(s) ofxfor which the series converges (i) absolutely?

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