数学问题：大一高数求极限

Question

这题怎么写啊要用到泰勒展开

Answer 1

根据泰勒展开
e^(x^2)=1+x^2+(x^4)/2+o(x^4)
cosx=1-(x^2)/2+(x^4)/24+o(x^4)
所以lim(x->0) [e^(x^2)+cosx-2]/(x^4)
=lim(x->0) [1+x^2+(x^4)/2+o(x^4)+1-(x^2)/2+(x^4)/24+o(x^4)-2]/(x^4)
=lim(x->0) [(x^2)/2+(13/24)*(x^4)+o(x^4)]/(x^4)
=lim(x->0) [1/(2x^2)+13/24+o(x^4)/(x^4)]
=+∞