limit x->infinity ln(x)/x — step-by-step solution

Compute the limit of

\frac{\ln (x)}{x}

x \to +∞

The limit of

\ln (x)

+∞

when

x \to +∞

For

\frac{\ln (x)}{x}

, we encounter the indeterminate form

\frac{+∞}{+∞}

x

tends to

+∞

By comparative growth,

x

grows faster than

\ln (x)

x \to +∞

So the limit of

\frac{\ln (x)}{x}

0

⁺ when

x \to +∞

▷Answer: $0$