f ( x ) = p n ( x ) + r n ( x ) Pol . Taylor f ( x ) = f ( a ) ⏟ a 0 + f ′ ( a ) ⏟ a 1 ( x − a ) + f ″ ( a ) 2 ! ⏟ a 2 ( x − a ) 2 + f ‴ ( a ) 3 ! ⏟ a 3 ( x − a ) 3 + . . . + f n ) ( a ) n ! ⏟ a n ( x − a ) n Pol . Maclaurin f ( x ) = f ( 0 ) + f ′ ( 0 ) x + f ″ ( 0 ) 2 ! x 2 + . . . + f n ) ( 0 ) n ! x n f ( x ) = p n ( x ) ⏟ Pol . Taylor + r n ( x ) ⏟ f n + 1 ) ( a ) ( n + 1 ) ! ( x − a ) n + 1 | Error | = | f ( x ) − f n ( x ) | = | r n ( x ) | {\displaystyle {\begin{aligned}&f(x)=p_{n}(x)+r_{n}(x)\\&{\text{Pol}}{\text{. Taylor}}\\&f(x)=\underbrace {f(a)} _{a_{0}}+\underbrace {f^{'}(a)} _{a_{1}}(x-a)+\underbrace {\frac {f^{''}(a)}{2!}} _{a_{2}}(x-a)^{2}+\underbrace {\frac {f^{'''}(a)}{3!}} _{a_{3}}(x-a)^{3}+...+\underbrace {\frac {f^{n)}(a)}{n!}} _{a_{n}}(x-a)^{n}\\&{\text{Pol}}{\text{. Maclaurin}}\\&f(x)=f(0)+f^{'}(0)x+{\frac {f^{''}(0)}{2!}}x^{2}+...+{\frac {f^{n)}(0)}{n!}}x^{n}\\&\\&f(x)=\underbrace {p_{n}(x)} _{{\text{Pol}}{\text{. Taylor}}}+\underbrace {r_{n}(x)} _{{\frac {f^{n+1)}(a)}{(n+1)!}}(x-a)^{n+1}}\\&\left|{\text{Error}}\right|=\left|f(x)-f_{n}(x)\right|=\left|r_{n}(x)\right|\\\end{aligned}}}
