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

解

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

- \frac{3}{5}

十進法表記

- 0.6

解答ステップ

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

最高の分母べき乗で割る:

\frac{- 3 - \frac{4}{x} + \frac{2}{x ^{3}}}{5 + \frac{4}{x} - \frac{2}{x ^{2}}}

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

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

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

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

= \frac{- 3}{5}

簡素化

= - \frac{3}{5}