Taylor series with Python and Sympy part 3. Full article at http://www.firsttimeprogrammer.blogspot.com/2015/03/taylor-series-with-python-and-sympy.html

taylor_series_p3.py

# Plot results
def plot():
    x_lims = [-5,5]
    x1 = np.linspace(x_lims[0],x_lims[1],800)
    y1 = []
    # Approximate up until 10 starting from 1 and using steps of 2
    for j in range(1,10,2):
        func = taylor(f,0,j)
        print('Taylor expansion at n='+str(j),func)
        for k in x1:
            y1.append(func.subs(x,k))
        plt.plot(x1,y1,label='order '+str(j))
        y1 = []
    # Plot the function to approximate (sine, in this case)
    plt.plot(x1,np.sin(x1),label='sin of x')
    plt.xlim(x_lims)
    plt.ylim([-5,5])
    plt.xlabel('x')
    plt.ylabel('y')
    plt.legend()
    plt.grid(True)
    plt.title('Taylor series approximation')
    plt.show()

plot()