limit as x approaches-4-of (-4x^3)/(4+x)

解

x \to - 4 - lim (\frac{- 4 x ^{3}}{4 + x})

\infty

解答ステップ

x \to - 4 - lim (\frac{- 4 x ^{3}}{4 + x})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= - 4 \cdot x \to - 4 - lim (\frac{x ^{3}}{4 + x})

\frac{x ^{3}}{4 + x} = x^{3} \frac{1}{4 + x}

= - 4 \cdot x \to - 4 - lim (x^{3} \frac{1}{4 + x})

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

不定形式の場合を除く

= - 4 \cdot x \to - 4 - lim (x^{3}) \cdot x \to - 4 - lim (\frac{1}{4 + x})

x \to - 4 - lim (x^{3}) = - 64

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

= - 4 (- 64) (- \infty)

無限大の特性を適用する:

c \cdot (- \infty) = - \infty

= \infty