What is the limit as x approaches 3+of (ln(x))/(x-3) ?

The limit as x approaches 3+of (ln(x))/(x-3) is infinity

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limit as x approaches 3+of (ln(x))/(x-3)

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

\infty

Solution steps

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

\frac{ln ( x )}{x - 3} = ln (x) \frac{1}{x - 3}

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

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

x \to 3 + lim (ln (x)) = ln (3)

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

= ln (3) \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

What is the limit as x approaches 3+of (ln(x))/(x-3) ?
The limit as x approaches 3+of (ln(x))/(x-3) is infinity