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Finding the value of constants in f(x) as x->0

  1. Feb 19, 2008 #1
    I'm not looking for the complete answer (from what I've read in the intro posts, you won't/shouldn't give it to me anyways)... I just need to figure out where to start. This is my first time taking calc, and I'm pretty lost. Thanks in advance.

    1. The problem statement, all variables and given/known data

    Find the values of the constants a and b such that

    lim (x[tex]\rightarrow[/tex]0) [ ( [tex]\sqrt{a+bx}[/tex] - [tex]\sqrt{3}[/tex] ) / x ] = [tex]\sqrt{3}[/tex]

    3. The attempt at a solution

    I've attempted to solve it a couple of ways in an algebraic style, but the fact that there are three 'variables' has me stumped. I also tried using the limit property that states the limit of h(x)=f(x)/g(x) as x->c is L/K (I hope I got that right.. hah.) but the fact that K ends up being zero screws that up...

    I'm just completely lost as to where I need to start the problem. I don't know if I should be solving for a variable, doing trial-and-error stuff, using some kind of limit property, etc.
     
  2. jcsd
  3. Feb 19, 2008 #2
    Let
    [tex]f(x)=\frac{\sqrt{a+b\,x}-\sqrt3}{x}=\frac{g(x)}{x}[/tex]
    and solve for [itex]g(x)[/itex]

    What's the limit [tex]\lim_{x\to 0}g(x)[/tex] ?
     
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