limit as x approaches infinity of (3x^2+2x-8)/(sqrt(4x^4-5x+4))

解

x \to \infty lim (\frac{3 x ^{2} + 2 x - 8}{4 x ^{4} - 5 x + 4})

\frac{3}{2}

十進法表記

1.5

解答ステップ

x \to \infty lim (\frac{3 x ^{2} + 2 x - 8}{4 x ^{4} - 5 x + 4})

最高の分母べき乗で割る:

\frac{3 + \frac{2}{x} - \frac{8}{x ^{2}}}{4 - \frac{5}{x ^{3}} + \frac{4}{x ^{4}}}

= x \to \infty lim \frac{3 + \frac{2}{x} - \frac{8}{x ^{2}}}{4 - \frac{5}{x ^{3}} + \frac{4}{x ^{4}}}

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{2}{x} - \frac{8}{x ^{2}} )}{lim _{x \to \infty} ( 4 - \frac{5}{x ^{3}} + \frac{4}{x ^{4}} )}

x \to \infty lim (3 + \frac{2}{x} - \frac{8}{x ^{2}}) = 3

x \to \infty lim (4 - \frac{5}{x ^{3}} + \frac{4}{x ^{4}}) = 2

= \frac{3}{2}