Lim (cos(x)/cos(2x))^(1/x^2)

наверно x -> 0 = lim (cos(x) / (1-2sin^2(x))^(1/x^2) = lim (cos(x))^(1/x^2) =  lim (1+cos(x) -1)^(1/x^2) = lim (( 1 + [cos(x) - 1]) ^ 1/[cos(x) - 1] ) ^ ([cos(x) - 1] / x^2) = e ^ lim (cos(x) - 1) /x^2 = e^-lim (1-cosx)/x^2 = e^-lim [2[sin(x/2)]^2/[4*(x/2)^2] = e^-1/2*lim [sin(x/2)/(x/2)]^2 = e^-(1/2)