limit as x approaches 0+of (-ln(1+6x))/x

解答

x \to 0 + lim (\frac{- ln ( 1 + 6 x )}{x})

- 6

求解步骤

x \to 0 + lim (\frac{- ln ( 1 + 6 x )}{x})

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

= - x \to 0 + lim (\frac{ln ( 1 + 6 x )}{x})

使用洛必达法则

= - x \to 0 + lim (\frac{\frac{6}{1 + 6 x}}{1})

代入值

x = 0

= - \frac{\frac{6}{1 + 6 \cdot 0}}{1}

化简

= - 6

t a y l or 3 x

\frac{\partial}{\partial x} (x^{2} + 4 y^{2})

\int sin (x) cos (x) x d x

x \to 1 + lim (\frac{5 x + 6}{x - 1})

a re a x = - 5, x = 1, y = 7 x, y = x^{2} - 8