limit as x approaches 0 of 1/(2xcsc(4x))

解

x \to 0 lim (\frac{1}{2 x csc ( 4 x )})

2

解答ステップ

x \to 0 lim (\frac{1}{2 x csc ( 4 x )})

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

= \frac{1}{2} \cdot x \to 0 lim (\frac{1}{x csc ( 4 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{1}{2} \cdot \frac{lim _{x \to 0} ( 1 )}{lim _{x \to 0} ( x csc ( 4 x ) )}

x \to 0 lim (1) = 1

x \to 0 lim (x csc (4 x)) = \frac{1}{4}

= \frac{1}{2} \cdot \frac{1}{\frac{1}{4}}

簡素化

\frac{1}{2} \cdot \frac{1}{\frac{1}{4}} : 2

= 2