2. TAYLOROV TEOREM SREDNJE VRIJEDNOSTI

RowBox[{TEOREM, , StyleBox[2., FontFamily -> Arial, FontVariations -> {Underline -> True}], & ... ^n + f^(n + 1)(c)/(n + 1) ! (x - a)^(n + 1) , c∈ (a, x) . f (x) = T_n (x) + R_n (x)

RowBox[{RowBox[{Definicija, , StyleBox[2., FontVariations -> {Underline -> True}],  &nbs ... (x) = f (a) + f^'(a)/1 ! (x - a) + f^''(a)/2 ! (x - a)^2 +... + f^(n)(a)/n ! (x - a)^n . 

RowBox[{RowBox[{RowBox[{Definicija, , StyleBox[3., FontVariations -> {Underline -> True}], ... ; n + 1 - stupnja zadan formulom R_n (x) = f^(n + 1)(c)/(n + 1) ! (x - a)^(n + 1) . 

TAYLOROVA FORMULA f (x) = f (a) + f^'(a)/1 ! (x - a) + f^''(a)/2 ! (x - a)^2 +... + f^ ... 1) , c∈ (a, x) . f (x) = T_n (x) + R_n (x)  Za a = 0, McLaurinova formula .

Ako funkcija ima derivacije svakog reda i ako    Underscript[ lim, x ... u McLaurinov red f (0) + f^'(0)/1 ! x + f^''(0)/2 ! x^2 +... + f^(n)(0)/n ! x^n +... Null

PRIMJERI
e^x =1+1/1 ! x + 1/2 ! x^2 +... + 1/n !x^n+...
sin x= 1/1 ! x - 1/3 ! x^3 + 1/5 ! x^5 ... + (-1)^n1/(2n - 1) !x^(2n - 1)+...

Created by Mathematica  (November 27, 2003)