kill(all)$

van=facebook.com/LearningCalculus$

via=AhmedAlBaron$

Problem:'limit(sin(1/csc(m))^(sin(1/sec(m))),m,%pi/2);

     Use 1/csc(u) = sin(u) and 1/sec(u) = cos(u)

e(m):=sin(m)^(sin(cos(m)));

sin(0)^sin(0);

Log(a,u):= log(u)/log(a);

Log(sin(m),sin(cos(m)));

f(m);g(m);

k:2;

f(m):=''(diff(sin(cos(m))*log(sin(m)),m,k));

g(m):=''(diff(log(sin(cos(m))),m,k));

for i:1 thru 2 do
(
    kill(f,g,m),
    f(m):=''(diff(sin(cos(m))*log(sin(m)),m,i)),
    g(m):=''(diff(log(sin(cos(m))),m,i)),
    errcatch( print(i, "f(m)", f(m))),
    errcatch( print(i, "g(m)", g(m))),
    errcatch( print(f(%pi/2))),
    errcatch( print(g(%pi/2)))
);