Question

求x->0lim(arctanx-x)/[xln(1+2x^2)]的极限

Answer 1

lim(x->0)(arctanx-x)/[xln(1+2x^2)]

=lim(x->0)(arctanx-x)/x^3

=lim(x->0)[1/(1+x^2)-1]/(3x^2)

=lim(x->0)-x^2/[(1+x^2)(3x^2)]

=lim(x->0)-x^2/[(3x^2)]

=-1/3