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人気のある微分積分 >

limit as x approaches 0+of 1/(xln(x^9))

解

x \to 0 + lim (\frac{1}{x ln ( x ^{9} )})

解

- \infty

解答ステップ

x \to 0 + lim (\frac{1}{x ln ( x ^{9} )})

ln (x^{9}) = 9 ln (x)

= x \to 0 + lim (\frac{1}{x \cdot 9 ln ( x )})

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

= \frac{1}{9} \cdot x \to 0 + lim (\frac{1}{x ln ( x )})

\frac{1}{x ln ( x )} = \frac{1}{x} \cdot \frac{1}{ln ( x )}

= \frac{1}{9} \cdot x \to 0 + lim (\frac{1}{x} \cdot \frac{1}{ln ( x )})

ロピタル向けに書き換える

= \frac{1}{9} \cdot x \to 0 + lim \frac{\frac{1}{x}}{\frac{1}{\frac{1}{l n ( x )}}}

ロピタルの定理を適用する

= \frac{1}{9} \cdot x \to 0 + lim (\frac{- \frac{1}{x ^{2}}}{\frac{1}{x}})

簡素化

\frac{- \frac{1}{x ^{2}}}{\frac{1}{x}} : - \frac{1}{x}

= \frac{1}{9} \cdot x \to 0 + lim (- \frac{1}{x})

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

= \frac{1}{9} (- x \to 0 + lim (\frac{1}{x}))

右側から

0

に近づく

x

の場合は,

x > 0 \Rightarrow x > 0

分母は右から0に近づく正の数量

= \frac{1}{9} (- \infty)

無限大の特性を適用する:

c \cdot (- \infty) = - \infty

= - \infty

グラフ

人気の例

y^'=-y/(x^2)+1/(x^2y^2)

y^{^{'}} = - \frac{y}{x ^{2}} + \frac{1}{x ^{2} y ^{2}}

limit as x approaches 6+of 1/((x-6)^2)

x \to 6 + lim (\frac{1}{( x - 6 ) ^{2}})

derivative of (3^{x^2}+x/(2^{x^2)})

\frac{d}{d x} (\frac{3 ^{x^{2}} + x}{2 ^{x^{2}}})

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\int \frac{2 ( csc ( x ) ) ^{2}}{cot ( x )} d x

integral from 0 to 3 of 3e^x

\int_{0}^{3} 3 e^{x} d x