limit as x approaches 5-of-2/(sqrt(5-x))

解答

x \to 5 - lim (- \frac{2}{5 - x})

- \infty

求解步骤

x \to 5 - lim (- \frac{2}{5 - x})

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

= - 2 \cdot x \to 5 - lim (\frac{1}{5 - x})

x

从左侧趋近于

5, x < 5 \Rightarrow 5 - x > 0

分母从右侧趋近于 0，为正值

= - 2 \cdot \infty

运用无穷大属性:

- c \cdot \infty = - \infty

= - \infty

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