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 squareroot terms, multiplying both numerator and denominator by the conjugate is a good strategy.
Lim (3 sqrt( x+9))/(x )
x>0
= Lim (3sqrt(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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