limit as x approaches pi/4 of (sin(x-pi/4))/(4x-pi)

解

x \to \frac{π}{4} lim (\frac{sin ( x - \frac{π}{4} )}{4 x - π})

\frac{1}{4}

十進法表記

0.25

解答ステップ

x \to \frac{π}{4} lim (\frac{sin ( x - \frac{π}{4} )}{4 x - π})

ロピタルの定理を適用する

= x \to \frac{π}{4} lim (\frac{cos ( x - \frac{π}{4} )}{4})

値を挿入する

x = \frac{π}{4}

= \frac{cos ( \frac{π}{4} - \frac{π}{4} )}{4}

cos (\frac{π}{4} - \frac{π}{4}) = 1

= \frac{1}{4}