import numpy as np
import matplotlib.pyplot as plt

x = 1e3
a = np.linspace(0,2,100)
y = (1 + a/x -4/x**2)**(2*x)
z = ((np.exp(3)))*np.ones(100)
bx=plt.plot(a,z, label = 'e^3')
plt.plot(a,y, label = 'Limit value')

sol = np.zeros((2,1))
sol[0] = 3.0/2.0
sol[1] = np.exp(3)

#Display solution 
A = np.around(sol[0],decimals=2)
B = np.around(sol[1],decimals=2)


plt.plot(A,B,'o')
for xy in zip(A,B):
	plt.annotate('(%s, %s)' % xy, xy=xy, xytext=(30,0), textcoords='offset points')

plt.grid()
plt.legend([bx[0]],['$e^3$'], loc='best',prop={'size':11})
plt.xlabel('$a$')
plt.ylabel('$\\left(1 + \\frac{a}{x} - \\frac{4}{x^2}\\right)^{2x}$')
plt.savefig('../figs/ee16b1004.eps')
plt.show()


	

