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

The limit as x approaches infinity of sqrt(9x^2+x)-3 is infinity

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limit as x approaches infinity of sqrt(9x^2+x)-3

x \to \infty lim (9 x^{2} + x - 3)

\infty

Solution steps

x \to \infty lim (9 x^{2} + x - 3)

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= x \to \infty lim (9 x^{2} + x) - x \to \infty lim (3)

x \to \infty lim (9 x^{2} + x) = \infty

x \to \infty lim (3) = 3

= \infty - 3

Apply Infinity Property:

\infty - c = \infty

= \infty

What is the limit as x approaches infinity of sqrt(9x^2+x)-3 ?
The limit as x approaches infinity of sqrt(9x^2+x)-3 is infinity