calculus
posted by joc on .
What is the limit as x approaches infinity of radical (9x*2+x)3x?

I assume you mean
radical (9x²+x)3x
Multiply top and bottom by the conjugate
[√(9x²+x)3x]
=[√(9x²+x)3x]*[√(9x²+x)+3x] / √[(9x²+x)+3x]
=(9x²+x9x²)/[√(9x²+x)+3x]
=x/[√(9x²+x)+3x]
Now evaluate the limit as x>∞
Lim x/[√(9x²+x)+3x]
= x / 6x
= 1/6