How does Limit in mma work?

*To*: mathgroup at yoda.physics.unc.edu*Subject*: How does Limit in mma work?*From*: ken yip <yip-ken at cs.yale.edu>*Date*: Thu, 19 Sep 91 18:32:00 EDT

I was trying to understand how mma deals with the improper integral Integrate[Sqrt[(x + 1)/(1 - x )], {x,-1,1}] It seems to get stuck while evaluating the limit: In[22]:= Integrate[Sqrt[(x + 1)/(1 - x )], {x,-1,b}] Sqrt[1 - b] Out[22]= Pi - Sqrt[2 - (1 - b)] Sqrt[1 - b] - 2 ArcSin[-----------] Sqrt[2] In[23]:= Limit[%, b->1] Can anyone explain to me why it has trouble? Ken