What is the limit as x approaches infinity of radical (9x*2+x)-3x?

Answer 1

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+x-9x²)/[√(9x²+x)+3x]
=x/[√(9x²+x)+3x]

Now evaluate the limit as x->∞
Lim x/[√(9x²+x)+3x]
= x / 6x
= 1/6