F07-1205-T1-solutions

F07-1205-T1-solutions - F07 NAME f Hx L 2 Math 1205 Test 1...

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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 Æ 3 f H x L exists and is = +• FALSE lim x Æ 4 + f H x L = 1 FALSE lim x Æ 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 Æ 5 f H x L exists TRUE x = 3 is a vertical asymptote TRUE lim x Æ 2 - f H x L lim x Æ 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 Æ 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 Ø 2 x 2 - a x + a + 1 x - 2 must exist. Evaluate the limit in this case(s).
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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 Ø 2 x 2 - a x + a + 1 x - 2 =lim x Ø 2 x 2 - 5 x + 6 x - 2 = lim x Ø 2 H x - 2 L H x - 3 L x - 2 = lim x Ø 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 x oe @ 0, 1 D . For what value(s) of c must lim x Ø c f H x L exist? Determine the corresponding limit value(s).
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