What is the limit as x approaches 0+of x-1/x+3 ?

The limit as x approaches 0+of x-1/x+3 is -infinity

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limit as x approaches 0+of x-1/x+3

x \to 0 + lim (x - \frac{1}{x} + 3)

- \infty

Solution steps

x \to 0 + lim (x - \frac{1}{x} + 3)

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 (x) - x \to 0 + lim (\frac{1}{x}) + x \to 0 + lim (3)

x \to 0 + lim (x) = 0

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

x \to 0 + lim (3) = 3

= 0 - \infty + 3

Simplify

0 - \infty + 3 : - \infty

= - \infty

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What is the limit as x approaches 0+of x-1/x+3 ?
The limit as x approaches 0+of x-1/x+3 is -infinity