What is the limit as x approaches 0-of 6/x-6/(|x|) ?

The limit as x approaches 0-of 6/x-6/(|x|) is -infinity

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limit as x approaches 0-of 6/x-6/(|x|)

x \to 0 - lim (\frac{6}{x} - \frac{6}{∣ x ∣})

- \infty

Solution steps

x \to 0 - lim (\frac{6}{x} - \frac{6}{∣ x ∣})

x

is negative when

x \to 0 -

. Therefore

∣ x ∣ = - x

= x \to 0 - lim (\frac{6}{x} - \frac{6}{- 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{6}{x}) - x \to 0 - lim (\frac{6}{- x})

x \to 0 - lim (\frac{6}{x}) = - \infty

x \to 0 - lim (\frac{6}{- x}) = \infty

= - \infty - \infty

Apply Infinity Property:

- \infty - \infty = - \infty

= - \infty

x \cdot y^{^{'}} + y = x^{4} \cdot y^{3}

\int t^{19} e^{- t^{20}} d t

\frac{5}{s ^{3} - 2 s ^{2} - 3 s}

(2005, 56), (2010, 59)

\int_{0}^{1} \frac{3}{x ^{2} - x - 2} d x

What is the limit as x approaches 0-of 6/x-6/(|x|) ?
The limit as x approaches 0-of 6/x-6/(|x|) is -infinity