Question

用洛必达法则求Lim(x->0+)（1/x）^x^2

用洛必达法则求Lim(x->0+)（1/x）^x²

Answer 1

lim(x→0+) (1/x)^(x²)
=e^lim(x→0+) x²ln(1/x)，令x=1/t
=e^lim(t→+∞) lnt/t²
=e^lim(t→+∞) (1/t)/(2t)
=e^(1/2)lim(t→+∞) 1/t²
=e^(1/2*0)
=1

Answer 2

=e^(x^2ln(1/x))=e^(ln(1/x)/x^(-2))
再对右边求一下就可以