Little-O Estimate for Real Function/Examples

Examples of Little-$\oo$ Estimates for Real Functions

Example: Sine Function at $+\infty$

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

$\forall x \in \R: \map f x = \sin x$

Then:

$\map f x = \map \oo x$

as $x \to \infty$.

Example: $x = \map \oo {x^2}$ at $+\infty$

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

$\forall x \in \R: \map f x = x$

Then:

$\map f x = \map \oo {x^2}$

as $x \to \infty$.