limit as x approaches infinity of ((-2)x^3+x^2+1)/((-3)x^4+2x^2+1)

解

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

0

解答ステップ

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

最高の分母べき乗で割る:

\frac{- \frac{2}{x} + \frac{1}{x ^{2}} + \frac{1}{x ^{4}}}{- 3 + \frac{2}{x ^{2}} + \frac{1}{x ^{4}}}

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

x \to \infty lim (- \frac{2}{x} + \frac{1}{x ^{2}} + \frac{1}{x ^{4}}) = 0

x \to \infty lim (- 3 + \frac{2}{x ^{2}} + \frac{1}{x ^{4}}) = - 3

= \frac{0}{- 3}

規則を適用

\frac{0}{a} = 0, a \neq = 0

= 0