limit as x approaches infinity of (5x+6x^2)/(3x-8)

解

x \to \infty lim (\frac{5 x + 6 x ^{2}}{3 x - 8})

\infty

解答ステップ

x \to \infty lim (\frac{5 x + 6 x ^{2}}{3 x - 8})

最高の分母べき乗で割る:

\frac{5 + 6 x}{3 - \frac{8}{x}}

= x \to \infty lim (\frac{5 + 6 x}{3 - \frac{8}{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} ( 5 + 6 x )}{lim _{x \to \infty} ( 3 - \frac{8}{x} )}

x \to \infty lim (5 + 6 x) = \infty

x \to \infty lim (3 - \frac{8}{x}) = 3

= \frac{\infty}{3}

無限大の特性を適用する:

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

= \infty