F07-1205-T1-solutions

F07-1205-T1-solutions - F07 Math 1205 -- Test 1 19 Sep 2007...

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Unformatted text preview: F07 Math 1205 -- Test 1 19 Sep 2007 NAME: SOLUTIONS ____ CRN : You will be graded on how well and fully you support your work! Use only methods from class . 1 2 3 4 5 6 x 1 2 f H x L 1 . [24] a) Let f H x L be defined by the graph given above. Mark each statement true or false . f H x L is continuous at x = 1 TRUE lim x A 3 f H x L exists and is = + FALSE lim x A 4 + f H x L = 1 FALSE lim x A 2- f H x L = 1 2 TRUE f H 1 L + f H 2 L + f H 3 L 3 = 1 TRUE lim x A 5 f H x L exists TRUE x = 3 is a vertical asymptote TRUE lim x A 2- f H x L lim x A 2 + f H x L TRUE f H x L is discontinuous at x = 1, 2, 3, 4, 5 FALSE x = 5 is a removable discontinuityof f TRUE lim x A 3 f H x L does not exist TRUE x = 4 is a removable discontinuityof f FALSE 2 . [9] Determine the value(s) of a for which lim x 2 x 2- a x + a + 1 x- 2 must exist. Evaluate the limit in this case(s). x = 2 as well. Thus, 2 2- 2 a + a + 1 = 0, or after rearranging, a=5. The expression becomes: x 2- 5 x + 6 x- 2 = H x- 2 L H x- 3 L x- 2 , so the limit exists for this value. lim x 2 x 2- a x + a + 1 x- 2 =lim x 2 x 2- 5 x + 6 x- 2 = lim x 2 H x- 2 L H x- 3 L x- 2 = lim x 2 H x- 3 L = - 1 3. [9] Suppose that H x- 1 L 2 f H x L cos p x 2 for all...
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F07-1205-T1-solutions - F07 Math 1205 -- Test 1 19 Sep 2007...

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