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

解

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

- \infty

解答ステップ

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

最高の分母べき乗で割る:

\frac{x}{- 1 + \frac{2}{x}}

= 2 \cdot x \to \infty lim (\frac{x}{- 1 + \frac{2}{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

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

x \to \infty lim (x) = \infty

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

= 2 \cdot \frac{\infty}{- 1}

簡素化

2 \cdot \frac{\infty}{- 1} : - \infty

= - \infty