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人気のある微分積分 >

limit as x approaches 0+of sqrt(x)ln(7x)

解

x \to 0 + lim (x ln (7 x))

解

0

解答ステップ

x \to 0 + lim (x ln (7 x))

ロピタル向けに書き換える

= x \to 0 + lim (\frac{ln ( 7 x )}{\frac{1}{x}})

ロピタルの定理を適用する

= x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{1}{2 x ^{\frac{3}{2}}}})

簡素化

\frac{\frac{1}{x}}{- \frac{1}{2 x ^{\frac{3}{2}}}} : - 2 x^{\frac{1}{2}}

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

値を挿入する

x = 0

= - 2 \cdot 0^{\frac{1}{2}}

簡素化

= 0

グラフ

人気の例

limit as x approaches 2-of (x^2+5)/(x+1)

x \to 2 - lim (\frac{x ^{2} + 5}{x + 1})

limit as x approaches 8+of 1/(8-x)

x \to 8 + lim (\frac{1}{8 - x})

limit as x approaches 2 of 5^x

x \to 2 lim (5^{x})

limit as x approaches 0+of ln(x^{1/x})

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

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

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