Question

[ln(1+ax³)]/(x-arcsinx)和(e的ax次方+x²-ax-1)/[xsin(x/4

Answer 1

展开一下就可以了

x-arcsinx=x-(x+x^3/6+o(x^3))

e^(ax)=1+ax+a^2x^2/2+o(x^2)

x->0

第一题=lim ax^3/[x-(x+x^3/6+o(x^3))]=ax^3/[-x^3/6+o(x^3)]=-6a

第二题=lim[1+ax+a^2x^2/2+o(x^2)+x^2-ax-1]/(x^2/4)

=lim[(2a^2+4)x^2+o(x^2)]/x^2

=2a^2+4