Big-O Estimate for Real Function/Examples

Examples of Big-$\OO$ Estimates for Real Functions

Example: $10 \times$ Function at $+\infty$

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

$\forall x \in \R: \map f x = 10 x$

Then:

$\map f x = \map \OO x$

as $x \to \infty$.

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:

$\map f x = \map \OO 1$

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 $x \to \infty$.