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

Let's evaluate the limit of

\exp (x) - x^{10}

when

x \to +∞

The limit of

\exp (x)

+∞

when

x \to +∞

The limit of

- x^{10}

-∞

when

x \to +∞

For

\exp (x) - x^{10}

, the limit takes the indeterminate form

+∞ + -∞

when

x

→

+∞

By comparative growth,

\exp (x)

grows faster than

x^{10}

x \to +∞

So the limit of

\exp (x) - x^{10}

+∞

when

x \to +∞

▷Answer: $+∞$