Run the following code to see how to compute a one-dimensional Taylor series with Sage.
var('x,k')
colors=['red', 'black', 'green', 'magenta']
x1 = pi/2
xmin = x1 - pi; xmax = x1 + pi
f(x) = sin(x)
p1 = plot(f, (xmin, xmax), color='blue')
Taylor_series_3(x) = f.taylor(x, x1, 3)
p1 += plot(Taylor_series_3, (xmin, xmax), legend_label='3',
color='red')
Taylor_series_5(x) = f.taylor(x, x1, 5)
p1 += plot(Taylor_series_5, (xmin, xmax), legend_label='5',
color='green')
Taylor_series_7(x) = f.taylor(x, x1, 7)
p1 += plot(Taylor_series_7, (xmin, xmax), legend_label='7',
color='black')
Taylor_series_7.show()
show(p1)The results are shown in the following screenshot:
