limit as t approaches 0 of (sin(1-cos(t)))/(1-cos(t))

解

t \to 0 lim (\frac{sin ( 1 - cos ( t ) )}{1 - cos ( t )})

1

解答ステップ

t \to 0 lim (\frac{sin ( 1 - cos ( t ) )}{1 - cos ( t )})

ロピタルの定理を適用する

= t \to 0 lim (\frac{cos ( 1 - cos ( t ) ) sin ( t )}{sin ( t )})

共通因数を約分する:

sin (t)

= t \to 0 lim (cos (1 - cos (t)))

値を挿入する

t = 0

= cos (1 - cos (0))

簡素化

cos (1 - cos (0)) : 1

= 1