Wed Jan 27 19:57:34 MET 1999
REDUCE 3.7, 15-Jan-99 ...
1: 1:
2: 2: 2: 2: 2: 2: 2: 2: 2:
3: 3: 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;
4: 4: 4: 4: 4: 4: 4: 4: 4:
Time for test: 9910 ms, plus GC time: 450 ms
5: 5:
Quitting
Wed Jan 27 19:58:12 MET 1999