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

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

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limit as x approaches 0+of ln(x)-1/x

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

- \infty

Solution steps

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

x \to 0 + lim (ln (x)) = - \infty

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

= - \infty - \infty

Apply Infinity Property:

- \infty - \infty = - \infty

= - \infty

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