limit as x approaches infinity of (3x^2-2x-5)/(x-4)

解

x \to \infty lim (\frac{3 x ^{2} - 2 x - 5}{x - 4})

\infty

解答ステップ

x \to \infty lim (\frac{3 x ^{2} - 2 x - 5}{x - 4})

最高の分母べき乗で割る:

\frac{3 x - 2 - \frac{5}{x}}{1 - \frac{4}{x}}

= x \to \infty lim (\frac{3 x - 2 - \frac{5}{x}}{1 - \frac{4}{x}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

不定形式の場合を除く

= \frac{lim _{x \to \infty} ( 3 x - 2 - \frac{5}{x} )}{lim _{x \to \infty} ( 1 - \frac{4}{x} )}

x \to \infty lim (3 x - 2 - \frac{5}{x}) = \infty

x \to \infty lim (1 - \frac{4}{x}) = 1

= \frac{\infty}{1}

無限大の特性を適用する:

\frac{\infty}{c} = \infty

= \infty