limit as x approaches infinity of (3x^2+10x-7)/(2x^2-5x)

解

x \to \infty lim (\frac{3 x ^{2} + 10 x - 7}{2 x ^{2} - 5 x})

\frac{3}{2}

十進法表記

1.5

解答ステップ

x \to \infty lim (\frac{3 x ^{2} + 10 x - 7}{2 x ^{2} - 5 x})

最高の分母べき乗で割る:

\frac{3 + \frac{10}{x} - \frac{7}{x ^{2}}}{2 - \frac{5}{x}}

= x \to \infty lim (\frac{3 + \frac{10}{x} - \frac{7}{x ^{2}}}{2 - \frac{5}{x}})

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} ( 3 + \frac{10}{x} - \frac{7}{x ^{2}} )}{lim _{x \to \infty} ( 2 - \frac{5}{x} )}

x \to \infty lim (3 + \frac{10}{x} - \frac{7}{x ^{2}}) = 3

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

= \frac{3}{2}