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})

ln (x) + \frac{1}{x} = ln (x) (1 + \frac{\frac{1}{x}}{ln ( x )})

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

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

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

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