# calculus

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

• calculus -

I assume you mean
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

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