limit as x approaches 0+of-(2+ln(x))/x

解答

x \to 0 + lim (- \frac{2 + ln ( x )}{x})

\infty

求解步骤

x \to 0 + lim (- \frac{2 + ln ( x )}{x})

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

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

\frac{2 + ln ( x )}{x} = (2 + ln (x)) \frac{1}{x}

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

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

不定型除外

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

x \to 0 + lim (2 + ln (x)) = - \infty

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

= - (- \infty) \cdot \infty

运用无穷大属性:

- (- \infty) \infty = \infty

= \infty