**Example**

In typical usage, the formal definition of *O* notation is not used directly; rather, the *O* notation for a function *f*(*x*) is derived by the following simplification rules:

- If
*f*(*x*) is a sum of several terms, the one with the largest growth rate is kept, and all others omitted. - If
*f*(*x*) is a product of several factors, any constants (terms in the product that do not depend on*x*) are omitted.

For example, let, and suppose we wish to simplify this function, using *O* notation, to describe its growth rate as *x* approaches infinity. This function is the sum of three terms: 6*x*4, −2*x*3, and 5. Of these three terms, the one with the highest growth rate is the one with the largest exponent as a function of *x*, namely 6*x*4. Now one may apply the second rule: 6*x*4 is a product of 6 and *x*4 in which the first factor does not depend on *x*. Omitting this factor results in the simplified form *x*4. Thus, we say that *f*(*x*) is a big-oh of (*x*4) or mathematically we can write *f*(*x*) = *O*(*x*4). One may confirm this calculation using the formal definition: let *f*(*x*) = 6*x*4 − 2*x*3 + 5 and *g*(*x*) = *x*4. Applying the formal definition from above, the statement that *f*(*x*) = *O*(*x*4) is equivalent to its expansion,

for some suitable choice of *x*_{0} and *M* and for all *x* > *x*_{0}. To prove this, let *x*_{0} = 1 and *M* = 13. Then, for all *x* > *x*_{0}:

so

Read more about this topic: Big O Notation

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**Example** may also refer to:

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*Example*, Florida rock band For Squirrels' sole major-label album, released in 1995- example.com, example.net, example.org, example.edu and .example, domain names reserved for use in documentation as examples
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*Example*(P165), an Archer-class patrol and training vessel of the British Royal Navy *The Example*, a 1634 play by James Shirley*The Example*(comics), a 2009 graphic novel by Tom Taylor and Colin Wilson

### Famous quotes containing the word example:

“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, *example* by *example*, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”

—Marcel Proust (1871–1922)