limit as x approaches 0+of 2/(ln(x))

解

x \to 0 + lim (\frac{2}{ln ( x )})

0

解答ステップ

x \to 0 + lim (\frac{2}{ln ( x )})

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

= 2 \cdot x \to 0 + lim (\frac{1}{ln ( 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 0 +} ( 1 )}{lim _{x \to 0 +} ( ln ( x ) )}

x \to 0 + lim (1) = 1

x \to 0 + lim (ln (x)) = - \infty

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

簡素化

2 \cdot \frac{1}{- \infty} : 0

= 0