limit as x approaches 0 of csc(x)sin(sin(x))

解

x \to 0 lim (csc (x) sin (sin (x)))

1

解答ステップ

x \to 0 lim (csc (x) sin (sin (x)))

ロピタル向けに書き換える

= x \to 0 lim (\frac{sin ( sin ( x ) )}{\frac{1}{c s c ( x )}})

ロピタルの定理を適用する

= x \to 0 lim (\frac{cos ( sin ( x ) ) cos ( x )}{cos ( x )})

値を挿入する

x = 0

= \frac{cos ( sin ( 0 ) ) cos ( 0 )}{cos ( 0 )}

簡素化

\frac{cos ( sin ( 0 ) ) cos ( 0 )}{cos ( 0 )} : 1

= 1