limit as h approaches 0 of (cos((3pi)/2+h)-cos((3pi)/2))/(h)

解

h \to 0 lim (\frac{cos ( \frac{3 π}{2} + h ) - cos ( \frac{3 π}{2} )}{h})

1

解答ステップ

h \to 0 lim (\frac{cos ( \frac{3 π}{2} + h ) - cos ( \frac{3 π}{2} )}{h})

cos (\frac{3 π}{2} + h) - cos (\frac{3 π}{2}) = cos (h + \frac{3 π}{2})

= h \to 0 lim (\frac{cos ( h + \frac{3 π}{2} )}{h})

ロピタルの定理を適用する

= h \to 0 lim (\frac{cos ( h )}{1})

値を挿入する

h = 0

= \frac{cos ( 0 )}{1}

簡素化

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

= 1