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

解答

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

- \infty

求解步骤

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

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

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

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

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

= 4 (- \infty)

运用无穷大属性:

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

= - \infty

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

x \to - 8 lim (5)

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

x \to 2 lim (3 x^{2} - 3 x + 11)

x \to 0 - lim (\frac{2}{1 - 2 ^{\frac{1}{x}}})