Question

lim(1+x^2-cos2x)^(1/lnx),x趋近于0+

Answer 1

lim (1 + x^2－cos2x) ^ (1/lnx) (x—>0+)

＝lim [ x^2 + 2(sinx)^2 ] ^ (1/lnx)

＝lim [ x^2(1 + 2(sinx/x)^2) ] ^ (1/lnx)

＝lim (x^2)^(1/lnx) * lim [(1 + 2(sinx/x)^2) ]^(1/lnx)

＝lim (x^2)^(1/lnx) * 3^0 (x—>0+)

＝lim (e ^ 2t) ^ (1/t) (t＝lnx,t—>－∞)

＝e^2