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人気のある微分積分 >

limit as x approaches 0 of (1-cos(2x))/(10x^2)

解

x \to 0 lim (\frac{1 - cos ( 2 x )}{10 x ^{2}})

解

\frac{1}{5}

+1

十進法表記

0.2

解答ステップ

x \to 0 lim (\frac{1 - cos ( 2 x )}{10 x ^{2}})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{10} \cdot x \to 0 lim (\frac{1 - cos ( 2 x )}{x ^{2}})

ロピタルの定理を適用する

= \frac{1}{10} \cdot x \to 0 lim (\frac{2 sin ( 2 x )}{2 x})

ロピタルの定理を適用する

= \frac{1}{10} \cdot x \to 0 lim (\frac{4 cos ( 2 x )}{2})

値を挿入する

x = 0

= \frac{1}{10} \cdot \frac{4 cos ( 2 \cdot 0 )}{2}

簡素化

\frac{1}{10} \cdot \frac{4 cos ( 2 \cdot 0 )}{2} : \frac{1}{5}

= \frac{1}{5}

グラフ

人気の例

limit as x approaches-4 of (6x-2)(4x-5)

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limit as n approaches 0 of n/(n+1)

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