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

解

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

- \infty

解答ステップ

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

\frac{1 - 2 x}{x - 3} = (1 - 2 x) \frac{1}{x - 3}

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

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

不定形式の場合を除く

= x \to 3 + lim (1 - 2 x) \cdot x \to 3 + lim (\frac{1}{x - 3})

x \to 3 + lim (1 - 2 x) = - 5

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

= (- 5) \cdot \infty

無限大の特性を適用する:

- c \cdot \infty = - \infty

= - \infty