limit x->infinity exp(x)-x^10 — step-by-step solution

Let's evaluate the limit of

\exp (x) - x^{10}

when

x \to +∞

ⓘ We use a reference limit of the function exp

The limit of

\exp (x)

+∞

when

x \to +∞

ⓘ A quantity that grows without bound raised to a positive power still grows without bound, to a negative power it tends to 0

The limit of

- x^{10}

-∞

when

x \to +∞

For

\exp (x) - x^{10}

, we encounter the indeterminate form

+∞ + -∞

x

tends to

+∞

By comparative growth,

\exp (x)

grows faster than

x^{10}

x \to +∞

So the limit of

\exp (x) - x^{10}

+∞

when

x \to +∞

▶Limit:

+∞