lim[cos(a/x)]^(x^2)
=lim e^[x^2*lncos(a/x)]
=e^{lim x^2[cos(a/x)-1]}
=e^{lim x^2[-(a/x)^2/2]}
=e^[lim -a^2/2]
=e^(-a^2/2)