limit as x approaches 0+of cos(x)ln(x)

解答

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

- \infty

求解步骤

x \to 0 + lim (cos (x) ln (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 (cos (x)) \cdot x \to 0 + lim (ln (x))

x \to 0 + lim (cos (x)) = 1

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

= 1 \cdot (- \infty)

运用无穷大属性:

c \cdot (- \infty) = - \infty

= - \infty

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