What is the limit as x approaches 0-of 2/x-2/(|x|) ?

The limit as x approaches 0-of 2/x-2/(|x|) is -infinity

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limit as x approaches 0-of 2/x-2/(|x|)

x \to 0 - lim (\frac{2}{x} - \frac{2}{∣ x ∣})

- \infty

Solution steps

x \to 0 - lim (\frac{2}{x} - \frac{2}{∣ x ∣})

x

is negative when

x \to 0 -

. Therefore

∣ x ∣ = - x

= x \to 0 - lim (\frac{2}{x} - \frac{2}{- 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{2}{x}) - x \to 0 - lim (\frac{2}{- x})

x \to 0 - lim (\frac{2}{x}) = - \infty

x \to 0 - lim (\frac{2}{- x}) = \infty

= - \infty - \infty

Apply Infinity Property:

- \infty - \infty = - \infty

= - \infty

\frac{d}{d x} (6 x^{5} - 20 x^{4} + 20 x^{3} - 10 x + 4)

\int_{0}^{1} π (2 - \frac{1}{2} x)^{2} d x

\frac{\partial}{\partial t} (4 cos (t))

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

y = \frac{5}{x ^{2} + 1}, (2, 1)

What is the limit as x approaches 0-of 2/x-2/(|x|) ?
The limit as x approaches 0-of 2/x-2/(|x|) is -infinity