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Challenge Question

  1. Dec 26, 2011 #1
    I tutor an AP Calculus AB class at the library every week, and I recently gave the students a test on Limits and Continuity. The test was fairly straightforward, but some of the free-response questions were somewhat difficult. The students seemed to get the answers fine, but my friend/mentor seemed to disagree with the answer to one of the questions.

    The problem in question is the following limits question: [itex]lim_{x→0}[/itex] [itex]\frac{\sqrt{ax + b} – 2}{x} = 1[/itex]

    Given this equality, students were asked to find the values of a and b.

    My solutions were a = 4 and b = 4. However, this was disputed by my friend/mentor, who claimed that if x ≠ 0.

    Can somebody settle this dispute? What are the values of a and b?
     
  2. jcsd
  3. Dec 26, 2011 #2

    mathman

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    In order for the function to have a limit, the numerator must -> 0 as x -> 0. This forces √b = 2 (or b = 4). Using L'Hopital's rule, a = 2√b = 4.
     
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