WikiCards · Card list · Science cards · Taylor's theorem
Uncommon card · Science
Taylor's theorem, an Uncommon card
In calculus, Taylor's theorem gives an approximation of a k {\textstyle k} -times differentiable function around a given point by a polynomial of degree k {\textstyle k}, called the k {\textstyle k} -th-order Taylor polynomial.
- Rarity
- Uncommon
- Domain
- Science
- ATK
- 77
- DEF
- 62
- Power
- 139
- Wikipedia reads a year
- 170,000
Power 139 (ATK + DEF): stronger than 70 % of WikiCards cards.
The facts on the card
The card carries these facts from its Wikipedia article.
- For a smooth function, the Taylor polynomial is the truncation at the order k {\textstyle k} of the Taylor series of the function.
- The first-order Taylor polynomial is the linear approximation of the function, and the second-order Taylor polynomial is often referred to as the quadratic approximation.
- There are several versions of Taylor's theorem, some giving explicit estimates of the approximation error of the function by its Taylor polynomial.
Why it is Uncommon
Rarity in WikiCards follows a year of Wikipedia page views: the most read articles become Epic and Legendary cards. The Taylor's theorem article was read about 170,000 times in a year. ATK comes from the length of the article and DEF from its quality, so this card hits with 77 and blocks with 62: each hit it takes is cut by 25 %.
How to get Taylor's theorem
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Credits
Text : Wikipedia, Taylor's theorem (revision), CC BY-SA 4.0. Photo : Alessio Damato, CC BY-SA 3.0, Wikimedia Commons.