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人気のある微分積分 >

limit as x approaches 0 of (sin(x)(cos(x)-1))/(x^2)

解

x \to 0 lim (\frac{sin ( x ) ( cos ( x ) - 1 )}{x ^{2}})

解

0

解答ステップ

x \to 0 lim (\frac{sin ( x ) ( cos ( x ) - 1 )}{x ^{2}})

ロピタルの定理を適用する

= x \to 0 lim (\frac{cos ( x ) ( cos ( x ) - 1 ) - sin ^{2} ( x )}{2 x})

ロピタルの定理を適用する

= x \to 0 lim (\frac{- 2 sin ( 2 x ) + sin ( x )}{2})

値を挿入する

x = 0

= \frac{- 2 sin ( 2 \cdot 0 ) + sin ( 0 )}{2}

簡素化

\frac{- 2 sin ( 2 \cdot 0 ) + sin ( 0 )}{2} : 0

= 0

グラフ

人気の例

limit as x approaches infinity of x^3-4x^2+2

x \to \infty lim (x^{3} - 4 x^{2} + 2)

limit as x approaches 0 of (13e^{2x}-13)/(e^x-1)

x \to 0 lim (\frac{13 e ^{2 x} - 13}{e ^{x} - 1})

limit as h approaches 0 of ((2+h)^{4+h}-16)/h

h \to 0 lim (\frac{( 2 + h ) ^{4 + h} - 16}{h})

limit as x approaches 2 of sqrt(x^2-4x+1)

x \to 2 lim (x^{2} - 4 x + 1)

limit as x approaches x/2 of ((sin(x)-1))/(cos(x))

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