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

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

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

x \to 0 + lim (\frac{x - 2}{∣ x ∣})

- \infty

Solution steps

x \to 0 + lim (\frac{x - 2}{∣ x ∣})

x

is positive when

x \to 0 +

. Therefore

∣ x ∣ = x

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

Divide by highest denominator power:

1 - \frac{2}{x}

= x \to 0 + lim (1 - \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 (1) - x \to 0 + lim (\frac{2}{x})

x \to 0 + lim (1) = 1

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

= 1 - \infty

Apply Infinity Property:

c - \infty = - \infty

= - \infty

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