limit as x approaches 0+of 10xln(x)

解答

x \to 0 + lim (10 x ln (x))

0

求解步骤

x \to 0 + lim (10 x ln (x))

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

= 10 \cdot x \to 0 + lim (x ln (x))

改写以应用洛必达法则

= 10 \cdot x \to 0 + lim (\frac{ln ( x )}{\frac{1}{x}})

使用洛必达法则

= 10 \cdot x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{1}{x ^{2}}})

化简

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

= 10 \cdot x \to 0 + lim (- x)

代入值

x = 0

= 10 (- 0)

化简

= 0

x \to 2 - lim (\frac{- 3}{x ^{2} - 4})

l a pl a ce t r an s f or m 5 e - 3 (t - 2)

\frac{\partial}{\partial x} (3 x^{2} y + 2 x y^{2})

x \to 3 lim (tan (\frac{3 π}{4}))

\int \frac{1}{2 x + x} d x