Spring07-Test1 - Math 1205 Test 1 14 Feb 2007 NAME You will...

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Math 1205 -- Test 1 14 Feb 2007 NAME: You will be graded on how well and fully you support your work! Use only methods from class. - 4 - 3 - 2 - 1 1 2 3 4 x - 4 - 3 - 2 - 1 1 2 f H x L 1 . [13] a) Let f H x L be defined by the graph given above. Determine the following limits, writing + or - as appropri- ate. If a limit does not exist, explain why. lim x Ø-¶ f H x L lim x Ø 3 f H x L lim x Ø 4 f H x L lim x Ø 1 - f H x L lim x Ø 1 + f H x L lim x Ø 1 f H x L lim x Ø- 1 - f H x L lim x Ø- 1 f H x L lim x Ø 2 f H x L b) Using the definition of asymptotes, explain why x = - 1 is a vertical asymptote, but x = 3 is not. c) From the graph of f , state the x -values at which f is discontinuous and explain why.
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2 . [10] If we know that x cos H x L § sin H x L § x for 0 § x § p ÅÅÅÅ 2 , find lim x Ø 0 + sin H x L ÅÅÅÅÅÅÅÅÅÅÅÅÅ x . Support your answer. 3. [10 points each] If lim x Ø 6 f H x L g H x L exists, then must it be true that lim x Ø 6 f H x L g H x L = f H 6 L g H 6 L . Support or give a counter-example.
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