test1math1501 - 4) What is the limit lim x sin ( x ) x...

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Georgia Tech FALL 2009 Heinrich Matzinger QUIZ 1 FOR MATH 1501: CALCULUS I First name: last name Gtid Close book, no calculators allowed. Full 50 minutes time. Show your calculations! Do not use Hospital’s rule! 1) a) Draw the graph of the function f ( x ) := | x - 1 | x - 1 with domain [0 , 2]. At x = 1 we de±ne the function f to be equal to f (1) = 0. b) Is the function continuous at x = 1. Explain. 2) What is the limit lim x 0 + ( sin ( x )) 2 x equal to? Why? 3) What is the limit lim x 1 + sin ( x - 1) x - 1 equal to? Why?
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Unformatted text preview: 4) What is the limit lim x sin ( x ) x equal to? 5) What is the limit lim x -2 + x 2-8 x +12 x +2 equal to? Why? 6) What is the limit lim x -1 + x 2-8 x +12 x +2 equal to? Why? 7) What is the limit lim x + 1-cos x x 2 equal to. Why? 8) What is the limit lim x + 1-(cos x ) 2 x 2 equal to. Why? 9) What is the limit lim x + 1-cos(sin( x ) 2 ) x 3 equal to. Why?...
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