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人気のある微分積分 >

limit as x approaches 0 of (1-cos(8x))/(1-cos(3x))

解

x \to 0 lim (\frac{1 - cos ( 8 x )}{1 - cos ( 3 x )})

解

\frac{64}{9}

+1

十進法表記

7.11111 \dots

解答ステップ

x \to 0 lim (\frac{1 - cos ( 8 x )}{1 - cos ( 3 x )})

ロピタルの定理を適用する

= x \to 0 lim (\frac{8 sin ( 8 x )}{3 sin ( 3 x )})

ロピタルの定理を適用する

= x \to 0 lim (\frac{64 cos ( 8 x )}{9 cos ( 3 x )})

値を挿入する

x = 0

= \frac{64 cos ( 8 \cdot 0 )}{9 cos ( 3 \cdot 0 )}

簡素化

\frac{64 cos ( 8 \cdot 0 )}{9 cos ( 3 \cdot 0 )} : \frac{64}{9}

= \frac{64}{9}

グラフ

人気の例

limit as x approaches 3 of (x-3)^{x-3}

x \to 3 lim ((x - 3)^{x - 3})

limit as x approaches 0 of e^{cos(x)}

x \to 0 lim (e^{c o s (x)})

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

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

limit as t approaches 0 of ((cos(t))/(cos(2t)))^{1/(t^2)}

t \to 0 lim ((\frac{cos ( t )}{cos ( 2 t )})^{\frac{1}{t ^{2}}})

limit as x approaches 1 of x^3-2x

x \to 1 lim (x^{3} - 2 x)