limit as x approaches 0-of (cot(pix)sin(x))/(2sec(x))

解

x \to 0 - lim (\frac{cot ( π x ) sin ( x )}{2 sec ( x )})

\frac{1}{2 π}

十進法表記

0.15915 \dots

解答ステップ

x \to 0 - lim (\frac{cot ( π x ) sin ( x )}{2 sec ( 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{cot ( π x ) sin ( 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{1}{2} \cdot \frac{lim _{x \to 0 -} ( cot ( π x ) sin ( x ) )}{lim _{x \to 0 -} ( sec ( x ) )}

x \to 0 - lim (cot (π x) sin (x)) = \frac{1}{π}

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

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

簡素化

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

= \frac{1}{2 π}