limit as x approaches 0-of x+(|x|)/x

解答

x \to 0 - lim (x + \frac{∣ x ∣}{x})

- 1

求解步骤

x \to 0 - lim (x + \frac{∣ x ∣}{x})

当

x \to 0 -

时,

x

为负. 因此

∣ x ∣ = - x

= x \to 0 - lim (x + \frac{- x}{x})

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

不定型除外

= x \to 0 - lim (x) + x \to 0 - lim (\frac{- x}{x})

x \to 0 - lim (x) = 0

x \to 0 - lim (\frac{- x}{x}) = - 1

= 0 - 1

化简

= - 1

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