From: drhuang57@gmail.com   
      
   we know that if lim f(x) = A  and lim g(x) = B  then lim f(x)*g(x) = AB   
      
   from these programs we learn that lim sin(x) = lim cos(x) = [-1,1]   
   also of course lim sin(2*x) = [-1,1].   
   putting these results together with   
      
   sin(2*x) = 2*sin(x)*cos(x)   
      
   and take the limit as x->oo  we learn that   
   [-1,1]  = 2*[-1,1]*[-1,1] = [-2,2].   
      
   Above is what Mathematica say. It give   
   Lim sin(2x) = [-1,1]   
   Lim 2sin(x) cos(x) = [-2,2]   
      
   What is your CAS say?   
   U can try on http://mathHandbook.com   
      
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