limit as x approaches 2-of (x-4)/(x-2)

解答

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

\infty

求解步骤

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

\frac{x - 4}{x - 2} = (x - 4) \frac{1}{x - 2}

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

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

x \to 2 - lim (x - 4) = - 2

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

= (- 2) (- \infty)

运用无穷大属性:

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

= \infty

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

x \to 0 lim (\frac{tan ( 5 x )}{tan ( 7 x )})

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

x \to 1 lim (2 + x)

x \to 4 - lim (\frac{4 + 8}{2})