limit as x approaches 3-of (ln(x))/(x-3)

解

x \to 3 - lim (\frac{ln ( x )}{x - 3})

- \infty

解答ステップ

x \to 3 - lim (\frac{ln ( x )}{x - 3})

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

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

x \to 3 - lim (ln (x)) = ln (3)

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

= ln (3) (- \infty)

無限大の特性を適用する:

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

= - \infty