Asymptotically Equal Real Functions/Examples/(x + 1)^3 (x + 2)^4 and x^7

Example of Asymptotically Equal Real Functions

Let $f: \R \to \R$ be the real function defined as:

$\forall x \in \R: \map f x = \paren {x + 1}^3 \paren {x + 2}^4$

Let $g: \R \to \R$ be the real function defined as:

$\forall x \in \R: \map g x = x^7$

Then:

$f \sim g$

as $x \to +\infty$.

Proof

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Sources

• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): asymptotically equal