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人気のある微分積分 >

limit as x approaches 0 of [ 1/x-1/(ln(1+x))]

解

x \to 0 lim ([\frac{1}{x} - \frac{1}{ln ( 1 + x )}])

解

- \frac{1}{2}

+1

十進法表記

- 0.5

解答ステップ

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

簡素化

\frac{1}{x} - \frac{1}{ln ( 1 + x )} : \frac{ln ( x + 1 ) - x}{x ln ( x + 1 )}

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

ロピタルの定理を適用する

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

ロピタルの定理を適用する

= x \to 0 lim (\frac{- \frac{1}{( x + 1 ) ^{2}}}{\frac{x + 2}{( x + 1 ) ^{2}}})

値を挿入する

x = 0

= \frac{- \frac{1}{( 0 + 1 ) ^{2}}}{\frac{0 + 2}{( 0 + 1 ) ^{2}}}

簡素化

\frac{- \frac{1}{( 0 + 1 ) ^{2}}}{\frac{0 + 2}{( 0 + 1 ) ^{2}}} : - \frac{1}{2}

= - \frac{1}{2}

グラフ

人気の例

limit as x approaches 0 of (sin(x)+x)/x

x \to 0 lim (\frac{sin ( x ) + x}{x})

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

x \to 0 lim (- \frac{1}{∣ x ∣})

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

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

limit as x approaches 0 of (12+x)^x

x \to 0 lim ((12 + x)^{x})

limit as x approaches-1 of 3x+2

x \to - 1 lim (3 x + 2)