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Finding Values that Satisfy a Limit

  1. Oct 18, 2013 #1

    eumyang

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    Homework Helper

    This may be a dumb question, but I'll ask anyway...

    1. The problem statement, all variables and given/known data
    Find the values of a and b such that
    [itex]\lim_{x \rightarrow 0} \frac{\sqrt{a + bx} - \sqrt{3}}{x} = \sqrt{3}[/itex]

    2. Relevant equations
    N/A

    3. The attempt at a solution
    I already have the work and the solution. However, someone showed me a different way. Here are the first couple of steps:
    [itex]\lim_{x \rightarrow 0} \frac{\sqrt{a + bx} - \sqrt{3}}{x} = \sqrt{3}[/itex]
    [itex]\lim_{x \rightarrow 0} \left( \sqrt{a + bx} - \sqrt{3} \right) = \sqrt{3} \cdot x[/itex]
    [itex]\lim_{x \rightarrow 0} \sqrt{a + bx} = \sqrt{3} + \sqrt{3} \cdot x[/itex]
    I'm having a brain fart. Is multiplying both sides by x, and then adding sqrt 3 to both sides, legal?
     
  2. jcsd
  3. Oct 18, 2013 #2

    Office_Shredder

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    Gold Member

    On the second line, the left hand side is a number, and the right hand side is a function of x. Does that sound like two things that are going to be equal to you?
     
  4. Oct 18, 2013 #3

    eumyang

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    That's what I thought -- I'm just too d***ed sleep-deprived. Thanks for the confirmation.
     
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