I guess both of them are equal(in python/sympy):
from sympy import *
x = Symbol('x')
limit(sin(x)/x,x,0)
#(result 1)
limit(sin(1/x)*x,x,00)
#(result 0 !!!)
In actually, let y = 1/x, limit(sin(1/x)*x,x,00) = limit(sin(y)/y,y,0)
, right?
(in anaconda 64-bit,ipython notebook, python 2.7, sympy0.7.6)
Try to use oo (oo is infinity) instead of 00.
To more exactly, use sympy.oo
import sympy as sym
from IPython.display import display,Math
fx = (1+1/x)**x
lim_pnt = sym.oo
lim = sym.limit(fx,x,lim_pnt)
display(Math('\\lim_{x\\to %s} %s = %s' %(lim_pnt,sym.latex(fx),sym.latex(lim))))
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