limit as x approaches-infinity of (4-7x)/(2+3x)

解

x \to - \infty lim (\frac{4 - 7 x}{2 + 3 x})

- \frac{7}{3}

十進法表記

- 2.33333 \dots

解答ステップ

x \to - \infty lim (\frac{4 - 7 x}{2 + 3 x})

最高の分母べき乗で割る:

\frac{\frac{4}{x} - 7}{\frac{2}{x} + 3}

= x \to - \infty lim (\frac{\frac{4}{x} - 7}{\frac{2}{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

= \frac{lim _{x \to - \infty} ( \frac{4}{x} - 7 )}{lim _{x \to - \infty} ( \frac{2}{x} + 3 )}

x \to - \infty lim (\frac{4}{x} - 7) = - 7

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

= \frac{- 7}{3}

簡素化

= - \frac{7}{3}