#coding: utf-8

def f(x):
	return ( x / ( x*x + 1) )	
#return 4 * (( (x ** 2) - 4 ) / ( x - 2 ))

def poslimit(f, a):
	v = []
	for x in range((a)*1000+20,a*1000,-1):
		a = float(a)
		x = float(x)
		v.append(f(x/1000))
		#print "a:%s , x:%s, l:%s" % (a,x,f(x/1000))
	return min( [ round(y*100)/100.0 for y in v ] )

def neglimit(f, a):
	v = []
	for x in range((a)*1000-20,a*1000,1):
		a = float(a)
		x = float(x)
		v.append(f(x/1000))
		#print "a:%s , x:%s, l:%s" % (a,x,f(x/1000))
	return max( [ round(y*100)/100.0 for y in v ] )

def limitcalc(f, a):
	neg = neglimit(f,a)
	pos = poslimit(f,a)
	if pos == neg:
		print "Limite é %s" %neg
	else:
		print "O limite não existe. LimPos %s LimNeg %s" % ( pos, neg)

limitcalc(f, 2)

Limite é 0.4