limit as x approaches 0 of (6x)/(cot(x))

解

x \to 0 lim (\frac{6 x}{cot ( x )})

0

解答ステップ

x \to 0 lim (\frac{6 x}{cot ( x )})

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

= 6 \cdot x \to 0 lim (\frac{x}{cot ( 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

= 6 \cdot \frac{lim _{x \to 0} ( x )}{lim _{x \to 0} ( cot ( x ) )}

x \to 0 lim (x) = 0

x \to 0 lim (cot (x)) = \infty

= 6 \cdot \frac{0}{\infty}

簡素化

6 \cdot \frac{0}{\infty} : 0

= 0