wfg1.mw

restart; 1 

WFG1 

 

`:=`(f, proc (x) options operator, arrow; `+`(`/`(`*`(`/`(1, 10), `*`(`+`(`*`(20, `*`(arccos(`+`(x, `-`(1))))), `-`(sin(`+`(`*`(20, `*`(arccos(`+`(x, `-`(1))))))))))), `*`(Pi)), `-`(1)) end proc); -1;...
`:=`(f, proc (x) options operator, arrow; `+`(`/`(`*`(`/`(1, 10), `*`(`+`(`*`(20, `*`(arccos(`+`(x, `-`(1))))), `-`(sin(`+`(`*`(20, `*`(arccos(`+`(x, `-`(1))))))))))), `*`(Pi)), `-`(1)) end proc); -1;...
 

 

f(x) = `+`(`/`(`*`(`/`(1, 10), `*`(`+`(`*`(20, `*`(arccos(`+`(x, `-`(1))))), `-`(sin(`+`(`*`(20, `*`(arccos(`+`(x, `-`(1))))))))))), `*`(Pi)), `-`(1))
x[min] = 0, x[max] = 1 (1)
 

 

 

`:=`(delta, proc (x) options operator, arrow; `/`(`*`(sqrt(`+`(`-`(`/`(`*`(diff(f(x), x)), `*`(`+`(1, `*`(`^`(diff(f(x), x), 2))))))))), `*`(C)) end proc); -1; 'delta(x)' = simplify(delta(x), size) 

delta(x) = `+`(`/`(`*`(`/`(1, 10), `*`(`^`(`+`(`-`(`/`(`*`(200, `*`(`+`(`-`(1), cos(`+`(`*`(20, `*`(arccos(`+`(x, `-`(1)))))))), `*`(Pi))), `*`(`^`(`+`(`-`(`*`(x, `*`(`+`(x, `-`(2)))))), `/`(1, 2)), `... (2)
 

`:=`(C, evalf(int(sqrt(`+`(`-`(diff(f(x), x)))), x = x[min] .. x[max]))); -1; '`/`(1, `*`(C))' = `/`(1, `*`(C)) 

`/`(1, `*`(C)) = 1.156904027 (3)
 

 

limit(diff(f(x), x), x = x[min]) 

0 (4)
 

`:=`(H2, proc (x) options operator, arrow; `+`(`*`(diff(f(x), x), `*`(`+`(x, `-`(x[max])))), f(x)) end proc); -1 

`:=`(R2, Optimization:-Maximize(H2(x), x = x[min] .. x[max])); -1; 'R[2]' = R2 

R[2] = [.979474081409809738, [x = .527388045827146601]] (5)