limit as w approaches infinity of (2w^2-3w+4)/(5w^2+7w-1)

解

w \to \infty lim (\frac{2 w ^{2} - 3 w + 4}{5 w ^{2} + 7 w - 1})

\frac{2}{5}

十進法表記

0.4

解答ステップ

w \to \infty lim (\frac{2 w ^{2} - 3 w + 4}{5 w ^{2} + 7 w - 1})

最高の分母べき乗で割る:

\frac{2 - \frac{3}{w} + \frac{4}{w ^{2}}}{5 + \frac{7}{w} - \frac{1}{w ^{2}}}

= w \to \infty lim (\frac{2 - \frac{3}{w} + \frac{4}{w ^{2}}}{5 + \frac{7}{w} - \frac{1}{w ^{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 _{w \to \infty} ( 2 - \frac{3}{w} + \frac{4}{w ^{2}} )}{lim _{w \to \infty} ( 5 + \frac{7}{w} - \frac{1}{w ^{2}} )}

w \to \infty lim (2 - \frac{3}{w} + \frac{4}{w ^{2}}) = 2

w \to \infty lim (5 + \frac{7}{w} - \frac{1}{w ^{2}}) = 5

= \frac{2}{5}