limit as x approaches-infinity of (x^2+2)/(x^3+x^2-1)

解

x \to - \infty lim (\frac{x ^{2} + 2}{x ^{3} + x ^{2} - 1})

0

解答ステップ

x \to - \infty lim (\frac{x ^{2} + 2}{x ^{3} + x ^{2} - 1})

最高の分母べき乗で割る:

\frac{\frac{1}{x} + \frac{2}{x ^{3}}}{1 + \frac{1}{x} - \frac{1}{x ^{3}}}

= x \to - \infty lim (\frac{\frac{1}{x} + \frac{2}{x ^{3}}}{1 + \frac{1}{x} - \frac{1}{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{1}{x} + \frac{2}{x ^{3}} )}{lim _{x \to - \infty} ( 1 + \frac{1}{x} - \frac{1}{x ^{3}} )}

x \to - \infty lim (\frac{1}{x} + \frac{2}{x ^{3}}) = 0

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

= \frac{0}{1}

規則を適用

\frac{0}{a} = 0, a \neq = 0

= 0