Posted by sara on Sunday, February 19, 2012 at 9:31pm.
In general, when there is a sum or difference of square-root terms, multiplying both numerator and denominator by the conjugate is a good strategy.
Lim (3- sqrt( x+9))/(-x )
x->0
= Lim (3-sqrt(x+9))(3+sqrt(x+9))/[(-x)(3+sqrt(x+9)]
x->0
= Lim (9-(x+9))/[(-x)(3+sqrt(x+9)]
x->0
= Lim (-x)/[(-x)(3+sqrt(x+9)]
x->0
= Lim 1/(3+sqrt(x+9)
x->0
=1/6
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