What is the limit as x approaches infinity of ln(1/x) ?

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

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limit as x approaches infinity of ln(1/x)

x \to \infty lim (ln (\frac{1}{x}))

- \infty

Solution steps

x \to \infty lim (ln (\frac{1}{x}))

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

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

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

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

Apply the common limit:

x \to \infty lim (ln (x)) = \infty

= - \infty

ln (y^{s i n (x)} \cdot y)

- \frac{ln ( 1 - x ) - ln ( 2 )}{ln ( 2 )}

(\frac{1}{2}) lo g_{b} (a) - 5 lo g_{b} (c)

ln (\frac{100 + 0.11}{0.11})

ln (\frac{0.5}{1.6})

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