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

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

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

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

\infty

Solution steps

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

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

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

= \infty - (- \infty)

Apply Infinity Property:

\infty + \infty = \infty

= \infty

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