limit as x approaches-2+of (2x-1)/(x+2)

解答

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

- \infty

求解步骤

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

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

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

x \to - 2 + lim (2 x - 1) = - 5

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

= (- 5) \cdot \infty

运用无穷大属性:

- c \cdot \infty = - \infty

= - \infty