1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    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!

Homework Help: 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


    User Avatar
    Science Advisor
    Homework Helper

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook