limit as x approaches 7-of (x-8)/(x-7)

解答

x \to 7 - lim (\frac{x - 8}{x - 7})

\infty

求解步骤

x \to 7 - lim (\frac{x - 8}{x - 7})

\frac{x - 8}{x - 7} = (x - 8) \frac{1}{x - 7}

= x \to 7 - lim ((x - 8) \frac{1}{x - 7})

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 7 - lim (x - 8) \cdot x \to 7 - lim (\frac{1}{x - 7})

x \to 7 - lim (x - 8) = - 1

x \to 7 - lim (\frac{1}{x - 7}) = - \infty

= (- 1) (- \infty)

运用无穷大属性:

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

= \infty

x \to 2 lim (2 x^{2} - 3 x - 4)

x \to 2 lim (\frac{4}{3} x - \frac{1}{2})

x \to - 3 lim (- x - 4)

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

x \to 0 lim (\frac{sin ( \frac{3}{8} ) x}{x})