limit as x approaches 1-of (2x)/(ln(x))

解

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

- \infty

解答ステップ

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

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

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

\frac{x}{ln ( x )} = x \frac{1}{ln ( x )}

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

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

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

x \to 1 - lim (x) = 1

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

= 2 \cdot 1 \cdot (- \infty)

無限大の特性を適用する:

c \cdot (- \infty) = - \infty

= - \infty