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

Compute the limit of

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

x \to +∞

ⓘ When the exponent tends to +∞, a base greater than 1 gives an infinite limit, a base strictly between 0 and 1 gives a zero limit

The limit of

2^{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^{5}

+∞

when

x \to +∞

For

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

, we obtain the indeterminate form

\frac{+∞}{+∞}

x

tends to

+∞

Comparative growth shows that

2^{x}

dominates

x^{5}

x \to +∞

So the limit of

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

+∞

when

x \to +∞

▶Limit:

+∞