calculus
posted by sara on .
find lim x>0 3 sqrt x+9/x

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