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Solving limits algebraically

  1. Aug 3, 2010 #1
    1. The problem statement, all variables and given/known data

    Just brushing up on my calculus before I start college, but I'm having difficulty manipulating two different limit equations algebraically (sorry I can't find out how to put these into latex):

    1) lim (t->0) {1/[t*sqrt(1+t)]} - (1/t)

    2) lim (x->-4) [sqrt(x^2+9) - 5]/(x+4)

    3. The attempt at a solution

    don't know where to begin on (2), but for (1):

    mult (1/t) by sqrt(1+t) to match denominators, left with [1 - sqrt(1+t)]/[t*sqrt(1+t)]

    any hints?
  2. jcsd
  3. Aug 3, 2010 #2


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    Try multiplying the numerator and denominator by 1+sqrt(1+t). Expand out the numerator and see what happens.
  4. Aug 3, 2010 #3
    For 2), multiply the numerator and denominator by the conjugate of the numerator.
  5. Aug 3, 2010 #4
    Ah, both of you were spot on with the conjugates. Thanks for your help.
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