limit as x approaches 0 of (ln(1-5x))/x

解答

x \to 0 lim (\frac{ln ( 1 - 5 x )}{x})

- 5

求解步骤

x \to 0 lim (\frac{ln ( 1 - 5 x )}{x})

使用洛必达法则

= x \to 0 lim (\frac{- \frac{5}{1 - 5 x}}{1})

代入值

x = 0

= \frac{- \frac{5}{1 - 5 \cdot 0}}{1}

化简

\frac{- \frac{5}{1 - 5 \cdot 0}}{1} : - 5

= - 5

x \to \infty lim (a x + b)

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

x \to \frac{π}{3} - lim (1 - cos (3 x))

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