ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

limit as x approaches 0+of x^2(ln(x))^2

解

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

解

0

解答ステップ

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

指数の規則を適用する:

a^{n} \cdot b^{n} = (a \cdot b)^{n}

x^{2} (ln (x))^{2} = (x ln (x))^{2}

= x \to 0 + lim ((x ln (x))^{2})

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

不定形式の場合を除く

= (x \to 0 + lim (x ln (x)))^{2}

ロピタル向けに書き換える

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

ロピタルの定理を適用する

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

簡素化

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

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

値を挿入する

x = 0

= (- 0)^{2}

簡素化

= 0

グラフ

人気の例

limit as x approaches 0 of (-2)/(x^2)

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

limit as x approaches 2 of-2x+4

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

limit as x approaches 0-of (9sin(x))/x

x \to 0 - lim (\frac{9 sin ( x )}{x})

limit as θ approaches pi/6 of (sin(2θ))/(sin(θ)tan(θ))

θ \to \frac{π}{6} lim (\frac{sin ( 2 θ )}{sin ( θ ) tan ( θ )})

limit as x approaches infinity of 40

x \to \infty lim (40)