Taylor Polynomial Error Approximation: Given the function y=f(x), the Taylor series centered at the point x=x0 for the function is defined to be f(x)=f(x0)+f′(x0)(x−x0)+f″(x0)(x−x0)22+f‴(x0)(x−x0)33!+f(iv)...
If we approximate the Taylor series centred a of function f(x) by a polynomial of degree n Tn(x). Then f(x)=Tn(x)+Rn(x) where Rn(x) is called remainer or error term. The error Rn(x)≤M(x−a)n+1(n+1)! where |f(n+1)(c)|≤Ma...
Using a calculator, compute the value f(0.1, 0.1) and compare it to the value of the second order Taylor polynomial at (0.1,0.1). a) f(z, y) = 1/(x^2 + y^2 + 1 Let f (x) = square root {2 x + 1}. a) Compute the Taylor series ...