#1:  " ----------[ D e r i v e ]---------- "                User


        #2:  " ---------- Initialization ---------- "               User


        #3:  " ---------- Limits ---------- "                       User


        #4:  " Start with a famous example => e "                   User


                    /     1 \n
        #5:   lim   |1 + ---|                                       User
             n->inf \     n / 


        #6:  #e                                                 Simp(#5)


        #7:  " => 1/2 "                                             User


                   1 - COS(x) 
             lim  ------------
        #8:  x->0       2                                           User
                       x      


              1 
        #9:  ---                                                Simp(#8)
              2 


        User

        #10: " See Dominik Gruntz, _On Computing Limits in a Symbolic

               Manipulation System_, "


        User

        #11: " Ph.D. dissertation, Swiss Federal Institute of Technology,

               Zurich, "


        #12: " Switzerland, 1996. => 5 "                            User


                      x    x 1/x
        #13:  lim   (3  + 5 )                                       User
             x->inf             

Memory Full

        #14: " => 1 "                                               User


                          LOG(x)     
        #15:  lim   -----------------                               User
             x->inf  LOG(x) + SIN(x) 


        #16: ?                                                 Simp(#15)

        #17: " => - e^2   [Gruntz] "                                User


                        /         x*EXP(-x)        \          
                     EXP|--------------------------| - EXP(x) 
                        |              /       2 \ |          
                        |              |    2*x  | |          
        #18:            | EXP(-x) + EXP|- -------| |                User
                        \              \   x + 1 / /          
              lim   ------------------------------------------
             x->inf                      x                    

Aborted after 1 hour

        #19: " => 1/3   [Gruntz] "                                  User


                                                   2 2      
                          x*LOG(x)*LOG(x*EXP(x) - x )       
        #20:  lim   ----------------------------------------        User
             x->inf           2                3            
                     LOG(LOG(x  + 2*EXP(EXP(3*x *LOG(x))))) 

Aborted after 1 hour

        #21: " => 1/e   [Knopp, p. 73] "                            User


                     1    1/n
        #22:  lim   ---*n!                                          User
             n->inf  n       

Memory Full

        #23: " Rewrite the above problem slightly => 1/e "          User


                     1              1/n
        #24:  lim   ---*GAMMA(n + 1)                                User
             n->inf  n                 

Memory Full

        #25: " => 1   [Gradshteyn and Ryzhik 8.328(2)] "            User


                     GAMMA(z + a)                 
        #26:  lim   --------------*EXP(- a*LOG(z))                  User
             z->inf    GAMMA(z)                   


        #27: 1                                                 Simp(#26)


        #28: " => e^z   [Gradshteyn and Ryzhik 9.121(8)] "          User


                         /          z \
        #29:  lim   GAUSS|1, k, 1, ---|                             User
             k->inf      \          k /


        #30: ?                                                 Simp(#29)


                       /          z \
        #31:  lim   F21|1, k, 1, ---|                               User
             k->inf    \          k /


               z
        #32: #e                                                Simp(#31)


        #33: " => Euler's_constant   [Gradshteyn and Ryzhik 9.536] "User


                  /             1   \
        #34: lim  |ZETA(x) - -------|                               User
             x->1 \           x - 1 /


        #35: ?                                                 Simp(#34)


        #36: " => gamma(x)   [Knopp, p. 385] "                      User


                               x         
                              n          
              lim   ---------------------
        #37: n->inf       n    /     x \                            User
                     x*PRODUCT |1 + ---| 
                         k=1   \     k / 

Aborted after 1 hour

        User

        #38: " See Angus E. Taylor and W. Robert Mann, _Advanced Calculus_,

               Second Edition, "


        #39: " Xerox College Publishing, 1972, p. 125 => 1 "        User


                      x              
                     /         2     
                   x*/  EXP(- t ) dt 
        #40:          0                                             User
             lim  -------------------
             x->0               2    
                     1 - EXP(- x )   


        #41: 1                                                 Simp(#40)


        #42: " => [-1, 1] "                                         User


             /        x            x  \
        #43: | lim  -----,  lim  -----|                             User
             \x->0-  |x|   x->0+  |x| /


        #44: [-1, 1]                                           Simp(#43)


        #45: " => pi/2   [Richard Q. Chen] "                        User


              lim  ATAN(- LOG(x))
        #46: x->0+                                                  User


              pi 
        #47: ----                                              Simp(#46)
               2 


        #48: " ---------- Quit ---------- "                         User