What is the limit as x approaches 0-of 5/x-5/(|x|) ?

The limit as x approaches 0-of 5/x-5/(|x|) is -infinity

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limit as x approaches 0-of 5/x-5/(|x|)

x \to 0 - lim (\frac{5}{x} - \frac{5}{∣ x ∣})

- \infty

Solution steps

x \to 0 - lim (\frac{5}{x} - \frac{5}{∣ x ∣})

x

is negative when

x \to 0 -

. Therefore

∣ x ∣ = - x

= x \to 0 - lim (\frac{5}{x} - \frac{5}{- x})

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

With the exception of indeterminate form

= x \to 0 - lim (\frac{5}{x}) - x \to 0 - lim (\frac{5}{- x})

x \to 0 - lim (\frac{5}{x}) = - \infty

x \to 0 - lim (\frac{5}{- x}) = \infty

= - \infty - \infty

Apply Infinity Property:

- \infty - \infty = - \infty

= - \infty

What is the limit as x approaches 0-of 5/x-5/(|x|) ?
The limit as x approaches 0-of 5/x-5/(|x|) is -infinity