limit as x approaches-8+of (2x)/(x+8)

解答

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

- \infty

求解步骤

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

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

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

除以分母的最高次幂:

\frac{1}{1 + \frac{8}{x}}

= 2 \cdot x \to - 8 + lim (\frac{1}{1 + \frac{8}{x}})

x

从右侧趋近于

- 8, x > - 8 \Rightarrow 1 + \frac{8}{x} < 0

分母从左侧趋近于 0，为负值

= 2 (- \infty)

运用无穷大属性:

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

= - \infty

d er i v a t i v e f (x) = \frac{2}{4 x + 3}

d er i v a t i v e f (x) = \frac{1 - 3 x}{1 + 3 x}

x \to \frac{3}{4} lim (\frac{4 x ^{2} - 9}{2 x - 3})

\int_{0}^{3} 3 - x d x

(4 sin (x))^{^{'}}