Constants math problem

  1. Given a, b are constants and lim x approch 1, a root x+3 - b all over x-1 equals 1. Find a and b

    No clue how to answer this, but this is what I think i can do

    a) get rid of the sqrt
    b) apply limit

    See, the problem is I have to unknows so i dont know what to do
     
  2. jcsd
  3. Is this your problem?

    [tex]\lim_{x\rightarrow{1}} \frac{a\sqrt{x+3}-b}{x-1}=1[/tex]?
     
  4. Curious3141

    Curious3141 2,970
    Homework Helper

    If the version posted in LaTex is correct, note that the denominator goes to zero when x->1. For the quotient to have a finite limit, the numerator must also go to zero when x is set to 1.

    You get a simple linear relationship between a and b. ---(1)

    Now you can use L'Hopital's Rule to evaluate a limit of the form 0/0. So differentiate both numerator and denominator. You know that the quotient of these two is also going to be 1 at the limit x->1.

    So set x = 1 in that. The b term would have vanished, so you can now solve for a. Put that back in equation (1) and work out b, you're done.
     
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