limit as x approaches-3+of (-5x)/(x+3)

解答

x \to - 3 + lim (\frac{- 5 x}{x + 3})

\infty

求解步骤

x \to - 3 + lim (\frac{- 5 x}{x + 3})

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

= - 5 \cdot x \to - 3 + lim (\frac{x}{x + 3})

除以分母的最高次幂:

\frac{1}{1 + \frac{3}{x}}

= - 5 \cdot x \to - 3 + lim (\frac{1}{1 + \frac{3}{x}})

x

从右侧趋近于

- 3, x > - 3 \Rightarrow 1 + \frac{3}{x} < 0

分母从左侧趋近于 0，为负值

= - 5 (- \infty)

运用无穷大属性:

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

= \infty

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