Question

what is the limit as x approaches infinity of the square root of (9x^2+x)-3x

Answer 1

Do you mean: \(\lim_{x \rightarrow \infty} \sqrt{9x^2 + x} - 3x \)?

Answer 2

If so, try multiplying the limit by: \[ \frac{3x + \sqrt{9x^2 + x}}{3x + \sqrt{9x^2 + x}} \]That is, rationalize the expression first.

Answer 3

then after that, divide top/bottom by x
remember x = sqrt(x^2)