limit as x approaches-infinity of (4x^6)/(x^3-8)

解

x \to - \infty lim (\frac{4 x ^{6}}{x ^{3} - 8})

- \infty

解答ステップ

x \to - \infty lim (\frac{4 x ^{6}}{x ^{3} - 8})

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

= 4 \cdot x \to - \infty lim (\frac{x ^{6}}{x ^{3} - 8})

最高の分母べき乗で割る:

\frac{x ^{3}}{1 - \frac{8}{x ^{3}}}

= 4 \cdot x \to - \infty lim (\frac{x ^{3}}{1 - \frac{8}{x ^{3}}})

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

= 4 \cdot \frac{lim _{x \to - \infty} ( x ^{3} )}{lim _{x \to - \infty} ( 1 - \frac{8}{x ^{3}} )}

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

x \to - \infty lim (1 - \frac{8}{x ^{3}}) = 1

= 4 \cdot \frac{- \infty}{1}

簡素化

4 \cdot \frac{- \infty}{1} : - \infty

= - \infty