# 10.5 Taylor Polynomials # Art Belmonte, Summer 1996 # These are the shaded gray examples which appear in Section 10.5. > restart; taylor(sin(x), x=0, 6); p:=convert(", polynom); 3 5 6 x - 1/6 x + 1/120 x + O(x ) 3 5 p := x - 1/6 x + 1/120 x > taylor(sin(x), x=Pi/2, 8); p:=convert(", polynom); 2 4 6 1 - 1/2 (x - 1/2 Pi) + 1/24 (x - 1/2 Pi) - 1/720 (x - 1/2 Pi) + 8 O((x - 1/2 Pi) ) 2 4 6 p := 1 - 1/2 (x - 1/2 Pi) + 1/24 (x - 1/2 Pi) - 1/720 (x - 1/2 Pi) > diff(sin(x), x$8); subs(x=xi, "); sin(x) sin(xi) > evalf((Pi/2)^8 / 8!); .0009192602758 > plot({sin(x), p}, x=-Pi/2..3*Pi/2); >