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

解

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

- \frac{1}{2}

十進法表記

- 0.5

解答ステップ

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

最高の分母べき乗で割る:

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

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

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

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

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

= \frac{2}{- 4}

簡素化

\frac{2}{- 4} : - \frac{1}{2}

= - \frac{1}{2}