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人気のある微分積分 >

limit as x approaches 0 of (1-cos(7x))/(4x^2)

解

x \to 0 lim (\frac{1 - cos ( 7 x )}{4 x ^{2}})

解

\frac{49}{8}

+1

十進法表記

6.125

解答ステップ

x \to 0 lim (\frac{1 - cos ( 7 x )}{4 x ^{2}})

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

= \frac{1}{4} \cdot x \to 0 lim (\frac{1 - cos ( 7 x )}{x ^{2}})

ロピタルの定理を適用する

= \frac{1}{4} \cdot x \to 0 lim (\frac{7 sin ( 7 x )}{2 x})

ロピタルの定理を適用する

= \frac{1}{4} \cdot x \to 0 lim (\frac{49 cos ( 7 x )}{2})

値を挿入する

x = 0

= \frac{1}{4} \cdot \frac{49 cos ( 7 \cdot 0 )}{2}

簡素化

\frac{1}{4} \cdot \frac{49 cos ( 7 \cdot 0 )}{2} : \frac{49}{8}

= \frac{49}{8}

グラフ

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