limit as x approaches 0+of 8sqrt(x)ln(x)

解答

x \to 0 + lim (8 x ln (x))

0

求解步骤

x \to 0 + lim (8 x ln (x))

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

= 8 \cdot x \to 0 + lim (x ln (x))

改写以应用洛必达法则

= 8 \cdot x \to 0 + lim (\frac{ln ( x )}{\frac{1}{x}})

使用洛必达法则

= 8 \cdot x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{1}{2 x ^{\frac{3}{2}}}})

化简

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

= 8 \cdot x \to 0 + lim (- 2 x^{\frac{1}{2}})

代入值

x = 0

= 8 (- 2 \cdot 0^{\frac{1}{2}})

化简

= 0

d er i v a t i v e F (t) = (3 t - 1)^{4} (2 t + 1)^{- 3}

t y^{^{'}} + y = t^{4} y^{3}

\int (a x^{2} + b x + c) d x

t an g e n t y = \frac{2 x - 1}{x + 2}

\frac{d}{d x} (x^{2} (ln (x)))