reduce-historical/r37/log/mrvlimit.rlg

Sun Aug 18 19:28:33 2002 run on Windows
off exp;

 off mcd;


mrv_limit(e^x,x,infinity);


infinity


ex:=log(log(x)+log(log(x)))-log(log(x));


ex :=  - (log(log(x)) - log(log(log(x)) + log(x)))

ex:=ex/(log(log(x)+log(log(log(x)))));


ex := 

                                                                           -1
 - (log(log(x)) - log(log(log(x)) + log(x)))*log(log(log(log(x))) + log(x))

ex:=ex*log(x);


ex :=  - (log(log(x)) - log(log(log(x)) + log(x)))

                                     -1
      *log(log(log(log(x))) + log(x))  *log(x)


mrv_limit(e^-x,x,infinity);


0


mrv_limit(log(x),x,infinity);


infinity


mrv_limit(1/log(x),x,infinity);


0


a:=e^(1/x-e^-x)-e^(1/x);


       -1        - x
      x      - e
a := e   *(e         - 1)

a:=a/e^(-x);


           -1        - x
      x + x      - e
a := e       *(e         - 1)

 
mrv_limit(a,x,infinity) ;


-1
          % all of these are correct
mrv_limit(e^-x,x,infinity) ;


0

mrv_limit(log(x),x,infinity) ;


infinity

mrv_limit(1/log(x),x,infinity) ;


0


a:=e^(1/x-e^-x)-e^(1/x);


       -1        - x
      x      - e
a := e   *(e         - 1)

a:=a/e^(-x);


           -1        - x
      x + x      - e
a := e       *(e         - 1)

b:=e^x*(e^(1/x-e^-x)-e^(1/x));


           -1        - x
      x + x      - e
b := e       *(e         - 1)


%c:=e^x*(e^(1/x+e^(-x)+e^(-x^2))-e^(1/x-e^(-e^x)))
maxi1({e^(-x^2)},{e^x});


      2
   - x
{e     }


cc:= e^(log(log(x+e^(log(x)*log(log(x)))))/log(log(log(e^x+x+log(x)))));


                                 x   -1               log(x)
       log(log(log(log(x) + x + e )))  *log(log(log(x)       + x))
cc := e

 
b:=e^x*(e^(1/x-e^-x)-e^(1/x));


           -1        - x
      x + x      - e
b := e       *(e         - 1)


c:=e^x*(e^(1/x+e^(-x)+e^(-x^2))-e^(1/x-e^(-e^x)));


                           x         2
              -1        - e       - x      - x
         x + x      - e         e      + e
c :=  - e       *(e          - e              )


e^(log(log(x+e^(log(x)*log(log(x)))))/(log(log(log(e^x+x+log(x))))));


                           x   -1               log(x)
 log(log(log(log(x) + x + e )))  *log(log(log(x)       + x))
e


%% mrv_limit(ws,x,infinity);

aa:=e^(e^(e^x));


         x
        e
       e
aa := e

bb:=e^(e^(e^(x-e^(-e^x))));


                 x
              - e
          - e      + x
        e
       e
bb := e

ex1:=(e^x)*(e^((1/x)-e^(-x))-e^(1/x));


             -1        - x
        x + x      - e
ex1 := e       *(e         - 1)
  % returns -1 correct

ex2:=(e^x)*(e^((1/x)-e^(-x)-e^(-x^2))-e^((1/x)-e^(-e^x)));


                             x            2
                -1        - e          - x      - x
           x + x      - e          - e      - e
ex2 :=  - e       *(e          - e                 )
 % returns infinity

ex3:=e^(e^(x-e^-x)/(1-1/x))-e^(e^x);


                           - x
             x         - e     + x   -1     -1
            e      - e            *(x   - 1)
ex3 :=  - (e   - e                            )
 % returns - infinity

ex4:=e^(e^((e^x)/(1-1/x)))-e^(e^((e^x)/(1-1/x-(log(x))^(-log(x)))));


                 x         - log(x)    -1     -1         x   -1     -1
              - e *(log(x)          + x   - 1)        - e *(x   - 1)
            e                                       e
ex4 :=  - (e                                     - e                  )


ex5:=(e^(e^(e^(x+e^-x))))/(e^(e^(e^x)));


            - x
          e     + x     x
         e             e
        e           - e
ex5 := e


ex6:=(e^(e^(e^x)))/(e^(e^(e^(x-e^(-e^x)))));


                     x
                  - e
              - e      + x     x
            e                 e
         - e               + e
ex6 := e
   

ex7:=(e^(e^(e^x)))/(e^(e^(e^(x-e^(e^x)))));


                  x
                 e
              - e   + x     x
            e              e
         - e            + e
ex7 := e
       

ex8:=(e^(e^x))/(e^(e^(x-e^(-e^(e^x)))));


                     x
                    e
                 - e
             - e       + x    x
         - e               + e
ex8 := e


ex9:=((log(x)^2)*e^(sqrt(log(x))*((log(log(x)))^2)*e^((sqrt(log(log(x))))*(log(log(log(x)))^3))))/sqrt(x);


ex9 := 

                                            3
          sqrt(log(log(x)))*log(log(log(x)))                          2
  - 1/2  e                                   *sqrt(log(x))*log(log(x))        2
x      *e                                                              *log(x)


ex10:=((x*log(x))*(log(x*e^x-x^2))^2)/(log(log(x^2+2*e^(3*x^3*log(x)))));


                      3
                   3*x     2  -1       x        2
ex10 := log(log(2*x     + x ))  *log((e  - x)*x) *log(x)*x


misc1:=1/(e^(-x+e^-x))-e^x;


                   - x
          x    - e
misc1 := e *(e         - 1)
 % returns -1 correct

misc2:=(e^(1/x-e^-x)-e^(1/x))/(e^-x);


               -1        - x
          x + x      - e
misc2 := e       *(e         - 1)
 % returns -1 correct

misc3:=e^(-log(x+e^-x));


            - x     -1
misc3 := (e     + x)
 % returns 0 correct

misc4:=e^(x-e^x);


              x
           - e  + x
misc4 := e
 % returns 0 correct

% bb limit is infinity correct

mrv_limit(ex,x,infinity);


1
 %1

mrv_limit(ex1,x,infinity);


-1
 % -1

%% mrv_limit(ex2,x,infinity); % -1

%% mrv_limit(b,x,infinity); % -1

mrv_limit(a,x,infinity);


 - infinity
 

%% mrv_limit(ex3,x,infinity);

%% mrv_limit(ex4,x,infinity);

%% mrv_limit(ex5,x,infinity);  % 0

%% mrv_limit(ex6,x,infinity);

mrv_limit(misc1,x,infinity);


-1


mrv_limit(misc2,x,infinity);


 - infinity


mrv_limit(misc3,x,infinity);


0


mrv_limit(misc4,x,infinity);


0


end;


Time for test: 58043 ms, plus GC time: 3986 ms