if  
0  0  or no limit  if  
0  0  0  0  undeterminate 


0  
0  undeterminate  0  
0  undeterminate 

if ...  
undeterminate  if ...  
undeterminate  undeterminate  if ... 
In particular, the set of convergent sequences (with the same set ofindices) is a real vector space.
For limits of functions, we have a similar table; v.i. Theorem 4.1.
Noah DanaPicard 20071228