What is the limit as x approaches 0+of 1/x+1/(|x|) ?

The limit as x approaches 0+of 1/x+1/(|x|) is infinity

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limit as x approaches 0+of 1/x+1/(|x|)

x \to 0 + lim (\frac{1}{x} + \frac{1}{∣ x ∣})

\infty

Solution steps

x \to 0 + lim (\frac{1}{x} + \frac{1}{∣ x ∣})

x

is positive when

x \to 0 +

. Therefore

∣ x ∣ = x

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

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

= \infty + \infty

Apply Infinity Property:

\infty + \infty = \infty

= \infty

What is the limit as x approaches 0+of 1/x+1/(|x|) ?
The limit as x approaches 0+of 1/x+1/(|x|) is infinity