limit as x approaches infinity of (2x^2-9x-2)/(-5x^2-10x+3)

解

x \to \infty lim (\frac{2 x ^{2} - 9 x - 2}{- 5 x ^{2} - 10 x + 3})

- \frac{2}{5}

十進法表記

- 0.4

解答ステップ

x \to \infty lim (\frac{2 x ^{2} - 9 x - 2}{- 5 x ^{2} - 10 x + 3})

最高の分母べき乗で割る:

\frac{2 - \frac{9}{x} - \frac{2}{x ^{2}}}{- 5 - \frac{10}{x} + \frac{3}{x ^{2}}}

= x \to \infty lim (\frac{2 - \frac{9}{x} - \frac{2}{x ^{2}}}{- 5 - \frac{10}{x} + \frac{3}{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} ( 2 - \frac{9}{x} - \frac{2}{x ^{2}} )}{lim _{x \to \infty} ( - 5 - \frac{10}{x} + \frac{3}{x ^{2}} )}

x \to \infty lim (2 - \frac{9}{x} - \frac{2}{x ^{2}}) = 2

x \to \infty lim (- 5 - \frac{10}{x} + \frac{3}{x ^{2}}) = - 5

= \frac{2}{- 5}

簡素化

= - \frac{2}{5}