Home/Differential Calculus/Taylor series (introduction)/Lagrange remainderSection 11.3Lagrange remainderFormulaCopy LaTeXRn(x)=f(n+1)(c)(n+1)!(x−a)n+1,c between a and x, f(n+1) exists and is continuous on the open interval between a and xR_n(x)=\frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1},\qquad c\text{ between }a\text{ and }x,\ f^{(n+1)}\text{ exists and is continuous on the open interval between }a\text{ and }xRn(x)=(n+1)!f(n+1)(c)(x−a)n+1,c between a and x, f(n+1) exists and is continuous on the open interval between a and xRequires that f(n+1)f^{(n+1)}f(n+1) exists and is continuous on the open interval between aaa and xxx.c between a and x, f(n+1) exists and is continuous on the open interval between a and xc\text{ between }a\text{ and }x,\ f^{(n+1)}\text{ exists and is continuous on the open interval between }a\text{ and }xc between a and x, f(n+1) exists and is continuous on the open interval between a and xView detail →
FormulaCopy LaTeXRn(x)=f(n+1)(c)(n+1)!(x−a)n+1,c between a and x, f(n+1) exists and is continuous on the open interval between a and xR_n(x)=\frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1},\qquad c\text{ between }a\text{ and }x,\ f^{(n+1)}\text{ exists and is continuous on the open interval between }a\text{ and }xRn(x)=(n+1)!f(n+1)(c)(x−a)n+1,c between a and x, f(n+1) exists and is continuous on the open interval between a and xRequires that f(n+1)f^{(n+1)}f(n+1) exists and is continuous on the open interval between aaa and xxx.c between a and x, f(n+1) exists and is continuous on the open interval between a and xc\text{ between }a\text{ and }x,\ f^{(n+1)}\text{ exists and is continuous on the open interval between }a\text{ and }xc between a and x, f(n+1) exists and is continuous on the open interval between a and xView detail →