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

解

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

\infty

解答ステップ

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)

不定形式の場合を除く

= 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

無限大の特性を適用する:

\infty - c = \infty

= \infty