Posted by **sara** on Sunday, February 19, 2012 at 9:31pm.

find lim x->0 3- sqrt x+9/-x

- calculus -
**MathMate**, Sunday, February 19, 2012 at 10:26pm
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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