A value of h close to zero gives a good approximation to the slope of the tangent line, and smaller values ( in absolute value ) of h will, in general, give better approximations.

and a better approximation is

or, as an estimate of the better approximation,

Clearly, as the number of trials is increased, one might expect the relative frequency to become a better approximation of a " true frequency ".

The ratio of the perimeter to height of 1760 / 280 cubits equates to 2π to an accuracy of better than 0. 05 % ( corresponding to the well-known approximation of π as 22 / 7 ).

The term lossless is in contrast to lossy data compression, which only allows an approximation of the original data to be reconstructed, in exchange for better compression rates.

A better approximation is to take, the energy generation rate per unit mass, as ε is proportional to T < sub > I </ sub >< sup > 15 </ sup >, where T < sub > I </ sub > is the core temperature.

Given a function ƒ defined over the reals x, and its derivative ƒ < nowiki > '</ nowiki >, we begin with a first guess x < sub > 0 </ sub > for a root of the function f. Provided the function is reasonably well-behaved a better approximation x < sub > 1 </ sub > is

Both Legendre's and Dirichlet's's formulas imply the same conjectured asymptotic equivalence of π ( x ) and x / ln ( x ) stated above, although it turned out that Dirichlet's approximation is considerably better if one considers the differences instead of quotients.

In a handwritten note on a reprint of his 1838 paper " Sur l ' usage des séries infinies dans la théorie des nombres ", which he mailed to Carl Friedrich Gauss, Johann Peter Gustav Lejeune Dirichlet conjectured ( under a slightly different form appealing to a series rather than an integral ) that an even better approximation to π ( x ) is given by the offset logarithmic integral function Li ( x ), defined by

A shaping filter is sometimes used after the DAC with zero-order hold to make a better overall approximation.

When an accuracy better than one second is not required, UTC can be used as an approximation of UT1.

The twin prime conjecture would give a better approximation, as with the prime counting function, by

That is to say, the linearization of a real-valued function f ( x ) at the point x < sub > 0 </ sub > is a linear polynomial, and it may be possible to get a better approximation by considering a quadratic polynomial.

However, a better approximation that takes into account the primary's oblateness and the satellite's mass is:

The fact that most headphones are actually designed to have a notch in the 5 kHz region is not widely understood, and this may have led to errors in the assessment of binaural recordings, since flat headphones are not normally available, and ' high quality ' headphones incorporate the notch just like any others, though perhaps with a better approximation to that needed by the average ear.

Phong shading improves upon Gouraud shading and provides a better approximation of the shading of a smooth surface.

To a rough approximation, the Earth is a sphere, or to a much better approximation, an ellipsoid.

In this case, a better approximation can be obtained by reducing the absolute value of each difference between observed and expected frequencies by 0. 5 before squaring ; this is called Yates's correction for continuity.

The more spending rounds are offered, the better approximation the continuous, differentiable function is for its discrete counterpart.

Once that change is made, all of the 0. 01 elements will be added, giving 0. 99, and then the 1. 0 element will be added, yielding a rounded result of 2. 0 – a much better approximation of the real result.

As we have seen, the Babylonian ratio of 269 / 251 is a much better approximation, and it spans 18 full moon cycles which are equal to 18 basic 14-lunation cycles minus 1 month.

This is taken to be the best approximation that can be made to the real structure, though a better one may be made with addition of more structures.

This imperative, of course, is derived from consequential thinking: a better-informed agent is able to bring about better consequences.

This is a much better conclusion than might be derived from Figure 1.

They cover what are claimed to better ways for a Jew to live, based on what is not stated, but has been derived from the Hebrew Bible.

The later biographies and the biographies of subordinate emperors and usurpers are a tissue of lies and fiction, but the earlier biographies, derived primarily from now-lost earlier sources ( Marius Maximus or Ignotus ), are much better.

The show's gritty yet verbose humour derived largely from the tensions between Terry's cynical, everyman, working class personality and Bob's ambition to better himself and move to the middle class.

He wrote: The name was from the start Hoorn: not ( against better judgement ) derived from the weed Damphoorn, if t ' ghemeyne ghevoelen van noch heden hout ( De name was van eersten af Hoorn: niet ( behoudens beter oordeel ) van het kruyt Damphoorn, als t ' ghemeyne ghevoelen van noch heden hout ).

In the spring of 2006 some residents brought in B. Thomas Golisano, founder of Paychex, who expressed willingness to provide money to begin a competing wind farm which would give substantially more benefits ; specifically, the PILOT and payments to the landowners would be the same as or better than what was being offered by Airtricity, and residents of the town would receive part of the profits derived from the wind farm.

A long coiled compartment, rather than a short and straight one, provides more space for mapping pitches, so is therefore better adapted to the highly derived functions in mammalian hearing.

Mammalian derived envelope preparations have been better inducers of neutralizing antibody than candidates produced in yeast and bacteria.

Two derived terms are " newb ", a beginner who is willing to learn ; and " noob ", a derogatory name ( an alternate spelling for n00b ), though " newb " and " n00b " have become opposites of each other, meaning " newb " is plainly someone who is new to the game ( thus having the potential to get better ) and " n00b " is a player who both lacks skill and mainly fools around ( not wanting to become better ).

* That, from his observations of the Jovian moons he derived better periods of revolution and other orbital elements for them than did Galileo.

The Historical School contended that economists could develop new and better social laws from the collection and study of statistics and historical materials, and distrusted theories not derived from historical experience.

In contrast, the Pontiac Grand Prix and Chevrolet Monte Carlo, which were also derived from the intermediate A-body, were much better received because of their squared-off styling and formal rooflines with vertical windows.

His surname Baradaeus is derived from the ragged mendicant's garb patched up out of old saddle blankets, in which dress, the better to which disguise his spiritual functions from the eyes of the authorities, he performed his swift and secret journeys over Syria and Mesopotamia.

Although it is better known as " frankincense " to westerners, the resin is also known as olibanum, which is derived from the Arabic al-lubān ( roughly translated: " that which results from milking "), a reference to the milky sap tapped from the Boswellia tree.

While advocates claim that the shift is scientifically derived to better reflect the usage of the sands as a precursor to oil, environmental groups are claiming that this is simply a means of cloaking the issue behind friendlier terminology ( 5 ).

They are still considered the upper-class in Finland, especially in Helsinki, and have earned nicknames, such as " Svenska tala, bättre folk " ( Swedish speak, better people ), Hurri, derived from early wars when Swedish ( from Sweden ) troops attacking yelled " Hurrrrraaaaa!

He felt that he could help the team win with better technology derived from his race car experience, engineering background, as well as the abundant design and construction resources offered to him through his NASCAR connections.

A group of clones derived by crossing ' Italica ' with P. nigra ssp betulifolia at the Plantières Nursery near Metz in France in 1884 ; they are similar to ' Italica ' ( and often mistaken for it ) but with a slightly broader crown, and better adapted to the cool, humid climate of northwest Europe, where the true Lombardy poplar does not grow well.

In Spring 2008, Kurzweil launched the PC3 Performance Controller, which has next generation VAST synthesis technology derived from the K2xxx series but vastly improved with new features, new algorithms, virtual analog synthesis, sequencer, powerful effects processor based on Kurzweil KSP8 unit, and overall better sounds than previous Kurzweil synths.

It is unclear whether it was derived from the military term for stealing the better part of military rations and tossing the less appetizing portions away or if the military adopted the phrase from the political lexicon.

* derived key-keys computed by applying a predetermined hash algorithm or key derivation function to a password or, better, a passphrase.

* Goddessing is a recent contribution to Goddess vocabulary, possibly derived from the British journal of the same name, following from Mary Daly's linguistically suspect suggestion that deity is too dynamic, too much in process and changing continually, to be a noun, and should better be spoken as a verb ( Daly 1973 ).