limit as x approaches 0 of (5xcot(3x))/(2sec(x))

解

x \to 0 lim (\frac{5 x cot ( 3 x )}{2 sec ( x )})

\frac{5}{6}

十進法表記

0.83333 \dots

解答ステップ

x \to 0 lim (\frac{5 x cot ( 3 x )}{2 sec ( x )})

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

= \frac{5}{2} \cdot x \to 0 lim (\frac{x cot ( 3 x )}{sec ( 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

= \frac{5}{2} \cdot \frac{lim _{x \to 0} ( x cot ( 3 x ) )}{lim _{x \to 0} ( sec ( x ) )}

x \to 0 lim (x cot (3 x)) = \frac{1}{3}

x \to 0 lim (sec (x)) = 1

= \frac{5}{2} \cdot \frac{\frac{1}{3}}{1}

簡素化

\frac{5}{2} \cdot \frac{\frac{1}{3}}{1} : \frac{5}{6}

= \frac{5}{6}