limit as x approaches pi of (sin(x))/(1-\frac{x^2){pi^2}}

解

x \to π lim (\frac{sin ( x )}{1 - \frac{x ^{2}}{π ^{2}}})

\frac{π}{2}

十進法表記

1.57079 \dots

解答ステップ

x \to π lim (\frac{sin ( x )}{1 - \frac{x ^{2}}{π ^{2}}})

ロピタルの定理を適用する

= x \to π lim (\frac{cos ( x )}{- \frac{2 x}{π ^{2}}})

値を挿入する

x = π

= \frac{cos ( π )}{- \frac{2 π}{π ^{2}}}

簡素化

\frac{cos ( π )}{- \frac{2 π}{π ^{2}}} : \frac{π}{2}

= \frac{π}{2}