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人気のある微分積分 >

limit as x approaches 0+of xln(sin(2x))

解

x \to 0 + lim (x ln (sin (2 x)))

解

0

解答ステップ

x \to 0 + lim (x ln (sin (2 x)))

ロピタル向けに書き換える

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

ロピタルの定理を適用する

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

簡素化

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

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

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

ロピタル向けに書き換える

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

ロピタルの定理を適用する

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

値を挿入する

x = 0

= - 2 \cdot \frac{2 \cdot 0}{sec ^{2} ( 2 \cdot 0 ) \cdot 2}

簡素化

- 2 \cdot \frac{2 \cdot 0}{sec ^{2} ( 2 \cdot 0 ) \cdot 2} : 0

= 0

グラフ

人気の例

limit as x approaches 5 of 0/0

x \to 5 lim (\frac{0}{0})

limit as x approaches-3 of \sqrt[3]{x}

x \to - 3 lim (3 x)

limit as x approaches 10 of 7

x \to 10 lim (7)

limit as x approaches 0-of tan(x)+pi/2

x \to 0 - lim (tan (x) + \frac{π}{2})

limit as x approaches 0 of 2^{(1/(|x|))}

x \to 0 lim (2^{(\frac{1}{∣ x ∣})})