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

Let's evaluate the limit of

x - \ln (x)

when

x \to +∞

The limit of

- \ln (x)

-∞

when

x \to +∞

For

x - \ln (x)

, we encounter the indeterminate form

+∞ + -∞

x

tends to

+∞

By comparative growth,

x

grows faster than

\ln (x)

x \to +∞

So the limit of

x - \ln (x)

+∞

when

x \to +∞

▷Answer: $+∞$