limit as x approaches-2-of (3x-6)/(x+2)

解答

x \to - 2 - lim (\frac{3 x - 6}{x + 2})

\infty

求解步骤

x \to - 2 - lim (\frac{3 x - 6}{x + 2})

从

3 x - 6

分解出因式

3 x

3 x (1 - \frac{6}{3 x})

= x \to - 2 - lim (\frac{3 x ( 1 - \frac{6}{3 x} )}{x + 2})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 3 \cdot x \to - 2 - lim (\frac{x ( 1 - \frac{6}{3 x} )}{x + 2})

化简

\frac{x ( 1 - \frac{6}{3 x} )}{x + 2} : \frac{x - 2}{x + 2}

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

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

= 3 \cdot 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

= 3 \cdot 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

= 3 (- 4) (- \infty)

运用无穷大属性:

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

= \infty

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