limit as x approaches infinity of (x^2-1)/(8x^2-5)

解

x \to \infty lim (\frac{x ^{2} - 1}{8 x ^{2} - 5})

\frac{1}{8}

十進法表記

0.125

解答ステップ

x \to \infty lim (\frac{x ^{2} - 1}{8 x ^{2} - 5})

最高の分母べき乗で割る:

\frac{1 - \frac{1}{x ^{2}}}{8 - \frac{5}{x ^{2}}}

= x \to \infty lim (\frac{1 - \frac{1}{x ^{2}}}{8 - \frac{5}{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} ( 1 - \frac{1}{x ^{2}} )}{lim _{x \to \infty} ( 8 - \frac{5}{x ^{2}} )}

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

x \to \infty lim (8 - \frac{5}{x ^{2}}) = 8

= \frac{1}{8}