Açıklaması şöyle. Taylor serisi sanırım gerçek fonksiyonu hesaplamanın pahalı olduğu ancak yaklaşık bir değerin de işe yaradığı durumlarda kullanılır.
One practical reason for choosing a Taylor Series approximation of a function over the function itself is if you are able to compute using only the four arithmetic operations. For example, if you are asked to find the cosine of an angle and the only computing device you have is a four-function calculator, then you can get a good approximation of the cosine of the angle using the first few terms of the Taylor Series of the cosine function.
Açıklaması şöyle. Yani elimizde bir matematik kütüphanesi yoksa, Taylor Serisi kullanılarak trigonometric hesaplamalar yapılabilir.
A : Taylor series and other numerical methods are maybe less relevant from a formal education standpoint, but they are an incredibly nifty suite of tools to have in your back pocket if you ever find yourself programming in an environment without a proper math library (or need to approximate something weird like the error function).A : Taylor series are literally how computers compute all trig and log functions, except maybe some that use newton approximation (sqrt comes to mind). Of course there's lookup tables and all kinds of speedups, but if I ask you "calculate sin(x), you may add, subtract, multiply, and divide", how will you ever do it if you don't know about Taylor?
Örnek - sin
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exp(x)≈∑n=0∞xnn!=1+x+x22+x36+x424+…
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