limit as x approaches 0+of x^2ln(4x^2)

解答

x \to 0 + lim (x^{2} ln (4 x^{2}))

0

求解步骤

x \to 0 + lim (x^{2} ln (4 x^{2}))

改写以应用洛必达法则

= x \to 0 + lim (\frac{ln ( 4 x ^{2} )}{\frac{1}{x ^{2}}})

使用洛必达法则

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

化简

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

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

代入值

x = 0

= - 0^{2}

化简

= 0

x \to 2 lim (\frac{sin ( x - 2 )}{3 x - 6})

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

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

x \to 0 - lim ((1 - e^{x})^{x})

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