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人気のある微分積分 >

limit as x approaches 0 of (sin^2(3x))/(sin^2(5x))

解

x \to 0 lim (\frac{sin ^{2} ( 3 x )}{sin ^{2} ( 5 x )})

解

\frac{9}{25}

+1

十進法表記

0.36

解答ステップ

x \to 0 lim (\frac{sin ^{2} ( 3 x )}{sin ^{2} ( 5 x )})

ロピタルの定理を適用する

= x \to 0 lim (\frac{3 sin ( 6 x )}{5 sin ( 10 x )})

ロピタルの定理を適用する

= x \to 0 lim (\frac{18 cos ( 6 x )}{50 cos ( 10 x )})

値を挿入する

x = 0

= \frac{18 cos ( 6 \cdot 0 )}{50 cos ( 10 \cdot 0 )}

簡素化

\frac{18 cos ( 6 \cdot 0 )}{50 cos ( 10 \cdot 0 )} : \frac{9}{25}

= \frac{9}{25}

グラフ

人気の例

limit as x approaches 0+of x*sin(ln(x))

x \to 0 + lim (x \cdot sin (ln (x)))

limit as x approaches 2 of 1/x-1/2

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

limit as x approaches 1 of (x^x-1)/(x*ln(x))

x \to 1 lim (\frac{x ^{x} - 1}{x \cdot ln ( x )})

limit as x approaches 1 of xln(sin(x/2))

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

limit as x approaches 3 of x^2-6x+9

x \to 3 lim (x^{2} - 6 x + 9)