The following theorem looks like the corresponding theorem for sequences (v.s. 7.1). Recall that ``undeterminate'' means that there is no automatic conclusion in such a case, and that everything can happen, finite limit, infinite limit, no limit at all, etc.
if  
0  0  or no limit  if  
0  0  0  0  undeterminate 


0  
0  undeterminate  0  
0  undeterminate 

if ...  
undeterminate  if ...  
undeterminate  undeterminate  if ... 
We give now examples of the ``undeterminate'' cases, first of all in order to show why they are call undeterminate, then in order to show how they can be worked out.