limit x->infinity 2^x/x^5 — step-by-step solution

Let's evaluate the limit of

\frac{2^{x}}{x^{5}}

when

x \to +∞

The limit of

2^{x}

+∞

when

x \to +∞

The limit of

x^{5}

+∞

when

x \to +∞

For

\frac{2^{x}}{x^{5}}

, we encounter the indeterminate form

\frac{+∞}{+∞}

x

tends to

+∞

By comparative growth,

2^{x}

grows faster than

x^{5}

x \to +∞

So the limit of

\frac{2^{x}}{x^{5}}

+∞

when

x \to +∞

▷Result: $+∞$