limit as x approaches 3-of (ln(x))/(x-3)

解答

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

- \infty

求解步骤

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

\frac{ln ( x )}{x - 3} = ln (x) \frac{1}{x - 3}

= x \to 3 - lim (ln (x) \frac{1}{x - 3})

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 3 - lim (ln (x)) \cdot x \to 3 - lim (\frac{1}{x - 3})

x \to 3 - lim (ln (x)) = ln (3)

x \to 3 - lim (\frac{1}{x - 3}) = - \infty

= ln (3) (- \infty)

运用无穷大属性:

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

= - \infty

\frac{\partial}{\partial x} (- sin (y) + e^{x})

\frac{d}{d x} (x \cdot tan (x))

\int \frac{5}{( 3 x - 1 ) ^{3}} d x

\int \frac{e ^{- 5 x} + 3 x e ^{x}}{2} d x

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