limit as x approaches 8+of (x+5)/(x-8)

解答

x \to 8 + lim (\frac{x + 5}{x - 8})

\infty

求解步骤

x \to 8 + lim (\frac{x + 5}{x - 8})

\frac{x + 5}{x - 8} = (x + 5) \frac{1}{x - 8}

= x \to 8 + lim ((x + 5) \frac{1}{x - 8})

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 8 + lim (x + 5) \cdot x \to 8 + lim (\frac{1}{x - 8})

x \to 8 + lim (x + 5) = 13

x \to 8 + lim (\frac{1}{x - 8}) = \infty

= 13 \cdot \infty

运用无穷大属性:

c \cdot \infty = \infty

= \infty

x \to 0 lim (x + 2 - 1)

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

x \to \infty lim (\frac{2}{6 x})

x \to 0 lim (x cos (\frac{π}{x}))

x \to - \frac{π}{2} + lim (- 5 x - \frac{π}{2})