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人気のある微分積分 >

limit as x approaches 0+of sqrt(x)ln(6x)

解

x \to 0 + lim (x ln (6 x))

解

0

解答ステップ

x \to 0 + lim (x ln (6 x))

ロピタル向けに書き換える

= x \to 0 + lim (\frac{ln ( 6 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 3x^2

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

limit as x approaches 3 of (5-x)/(x-2)

x \to 3 lim (\frac{5 - x}{x - 2})

limit as x approaches 0 of xarctan(x)

x \to 0 lim (x arctan (x))

limit as x approaches pi/2 of arctan(x)

x \to \frac{π}{2} lim (arctan (x))

limit as h approaches 0 of 3x^2+3xh+h^2

h \to 0 lim (3 x^{2} + 3 x h + h^{2})