1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding Values that Satisfy a Limit

  1. Oct 18, 2013 #1


    User Avatar
    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

    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


    User Avatar
    Staff Emeritus
    Science Advisor
    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


    User Avatar
    Homework Helper

    That's what I thought -- I'm just too d***ed sleep-deprived. Thanks for the confirmation.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook