using the (limit or ratio of density function) compare the tail weight of the Weibull and inverse Weibull distribution

the pdf of the Weibull and inverse Weibull distribution

is the following:

Weibull -

??f(x)=?(x/?)?exp(?(x/?)?))/x??

while the inverse Weibull is

??f(x)=?(?/x)?exp(?(?/x)?))/x??

-1. With regard to the ratio of density functions, it is (with the inverse Weibull in the numerator and marking its parameters with asterisks) T*0*T x-T*-1e-(0*/2) 7* (T-T-(0*/2) +(x/0)7 TO TXT-le-(x/0)T The logarithm is (a/0) T - (0* / 20) 7" - (7+ 7*) Inx. The middle term goes to zero, so the issue is the limit of (x/0) - (7+7*) Inx, which is clearly infinite