limit as x approaches 5-of (x^5)/((x-5))

解答

x \to 5 - lim (\frac{x ^{5}}{( x - 5 )})

- \infty

求解步骤

x \to 5 - lim (\frac{x ^{5}}{x - 5})

\frac{x ^{5}}{x - 5} = x^{5} \frac{1}{x - 5}

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

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 5 - lim (x^{5}) \cdot x \to 5 - lim (\frac{1}{x - 5})

x \to 5 - lim (x^{5}) = 3125

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

= 3125 (- \infty)

运用无穷大属性:

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

= - \infty