Question

lim(1+3/x^2)^sin^2x x趋近正无穷

Answer 1

lim=lim[(1+3/x^2)]^{(x^2/3)*(3/x^2)*sin^2x}=e^{lim(3sin^2x)/x^2}=e^0=1 利用了当x为无穷大或x趋于0时,（1+1/x)^x=e