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人気のある微分積分 >

limit as x approaches 0 of (csc(-6x))/(csc(10x))

解

x \to 0 lim (\frac{csc ( - 6 x )}{csc ( 10 x )})

解

- \frac{5}{3}

+1

十進法表記

- 1.66666 \dots

解答ステップ

x \to 0 lim (\frac{csc ( - 6 x )}{csc ( 10 x )})

サイン, コサインで表わす

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

ロピタルの定理を適用する

= x \to 0 lim (\frac{cos ( 10 x ) \cdot 10}{- cos ( 6 x ) \cdot 6})

値を挿入する

x = 0

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

簡素化

\frac{cos ( 10 \cdot 0 ) \cdot 10}{- cos ( 6 \cdot 0 ) \cdot 6} : - \frac{5}{3}

= - \frac{5}{3}

グラフ

人気の例

limit as x approaches 0 of (ln(1+6x))/x

x \to 0 lim (\frac{ln ( 1 + 6 x )}{x})

limit as x approaches 1 of (x-1)ln(x)

x \to 1 lim ((x - 1) ln (x))

limit as x approaches-7 of (x^2+16x+63)/(-63-2x+x^2)

x \to - 7 lim (\frac{x ^{2} + 16 x + 63}{- 63 - 2 x + x ^{2}})

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

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

limit as x approaches pi of x-sin(x)

x \to π lim (x - sin (x))