Question

求一道高数题利用泰勒公式求x→0,lim(1+(1/2)x^2-sqr(1+x^2))/((cosx-e^(x)^2)s

Answer 1

x→0,1+(1/2)x^2-sqr(1+x^2)) = 1+(1/2)x^2-(1+(1/2)-(1/8)x^4+o(x^4))=-1/8*x^4+o(x^4)

(cosx-e^(x)^2)sin(x^2) = (1-(1/3)x^3+o(x^3)-(1+x^2+o(x^3)))(x^2+o(x^2)) = -x^4+o(x^4)

于是所求极限为 1/8