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

解

x \to 0 lim (\frac{cot ( π x ) \cdot 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 f (x) = x \to a + lim f (x) = L

の場合は

x \to a lim f (x) = L

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

x \to 0 + lim (\frac{cot ( π x ) sin ( x )}{2 sec ( x )}) = \frac{1}{2 π}

= \frac{1}{2 π}