103.sagews

var('x')
@interact
def taylor(f=sin(x)*e^(-x), order=slider([0..12],default=1), center  = (0,4)):
    p   = plot(f,-1,5, thickness=2)
    dot = point((center,f(center)),pointsize=80,rgbcolor=(1,0,0))
    ft = f.taylor(x,center,order)
    pt = plot(ft,-1, 5, color='green', thickness=2)
    html('$f(x)\;=\;%s\;\\approx\;%s$'%(latex(f), latex(ft)))
    show(dot + p + pt, ymin = -0.5, ymax = 1)

f  order  center

CPU time: 0.17 s, Wall time: 0.73 s

f=e^(-x)*sin(x)

f.taylor(x,0,4)

x - x^2 + x^3/3

[f.taylor(x,0,n) for n in [0..4]]

[0, x, x - x^2, x - x^2 + x^3/3, x - x^2 + x^3/3]