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人気のある微分積分 >

limit as x approaches 0 of (sin^2(3x))/(4x^2)

解

x \to 0 lim (\frac{sin ^{2} ( 3 x )}{4 x ^{2}})

解

\frac{9}{4}

+1

十進法表記

2.25

解答ステップ

x \to 0 lim (\frac{sin ^{2} ( 3 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{sin ^{2} ( 3 x )}{x ^{2}})

ロピタルの定理を適用する

= \frac{1}{4} \cdot x \to 0 lim (\frac{3 sin ( 6 x )}{2 x})

ロピタルの定理を適用する

= \frac{1}{4} \cdot x \to 0 lim (\frac{18 cos ( 6 x )}{2})

値を挿入する

x = 0

= \frac{1}{4} \cdot \frac{18 cos ( 6 \cdot 0 )}{2}

簡素化

\frac{1}{4} \cdot \frac{18 cos ( 6 \cdot 0 )}{2} : \frac{9}{4}

= \frac{9}{4}

グラフ

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