What is the limit as n approaches 1+of n/(ln(n)) ?

The limit as n approaches 1+of n/(ln(n)) is infinity

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limit as n approaches 1+of n/(ln(n))

n \to 1 + lim (\frac{n}{ln ( n )})

\infty

Solution steps

n \to 1 + lim (\frac{n}{ln ( n )})

\frac{n}{ln ( n )} = n \frac{1}{ln ( n )}

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

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

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

n \to 1 + lim (n) = 1

n \to 1 + lim (\frac{1}{ln ( n )}) = \infty

= 1 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

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