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人気のある微分積分 >

limit as x approaches 0 of 4/x sin(x/5)

解

x \to 0 lim (\frac{4}{x} sin (\frac{x}{5}))

解

\frac{4}{5}

+1

十進法表記

0.8

解答ステップ

x \to 0 lim (\frac{4}{x} sin (\frac{x}{5}))

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

= 4 \cdot x \to 0 lim (\frac{1}{x} sin (\frac{x}{5}))

簡素化

\frac{1}{x} sin (\frac{x}{5}) : \frac{sin ( \frac{x}{5} )}{x}

= 4 \cdot x \to 0 lim (\frac{sin ( \frac{x}{5} )}{x})

ロピタルの定理を適用する

= 4 \cdot x \to 0 lim (\frac{cos ( \frac{x}{5} ) \frac{1}{5}}{1})

値を挿入する

x = 0

= 4 \cdot \frac{cos ( \frac{0}{5} ) \frac{1}{5}}{1}

簡素化

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

= \frac{4}{5}

グラフ

人気の例

limit as x approaches 1 of (1+1/x)^x

x \to 1 lim ((1 + \frac{1}{x})^{x})

limit as x approaches 4 of 3x+2+2x

x \to 4 lim (3 x + 2 + 2 x)

limit as x approaches 0+of x^{-4}

x \to 0 + lim (x^{- 4})

limit as x approaches-infinity of 2^{2x}

x \to - \infty lim (2^{2 x})

limit as x approaches 0 of (1/x)/1

x \to 0 lim (\frac{\frac{1}{x}}{1})