from math import exp


#def f(x):
#    return exp(x)

f = lambda x: exp(x)  # f(x)
df = lambda x: exp(x) # f'(x)
a = 1

exact = df(a)

for k in range(1, 15):
    h = 10**(-k)
    approx = (f(a+h)-f(a))/h
    error = abs(exact - approx)
    print "h: %3e  error: %5e" %(h, error)