1、cosx=1-x^2/2+o(x^2)
ln(1+x)=x-x^2/2+o(x^2)
所以原式=lim(x→0)[(1-x^2/2+o(x^2))(x-x^2/2+o(x^2))-x]/x^2
=lim(x→0)[x-x^2/2+o(x^2)-x]/x^2
=lim(x→0)[(-x^2/2+o(x^2)]/x^2
=lim(x→0)(-1/2+o(1))
=-1/2
2、e^x=1+x+x^2/2!+x^3/3!+o(x^3)
原式=lim(x→0)[1+x+x^2/2!+x^3/3!+o(x^3)-x-x^2]/x^3 (sinx~x)
=lim(x→0)[1-x^2/2+o(x^2)]/x^3
=∞
第二个题写错了吧?还是我理解错了?