Find the equivalent infinitesimal of (1 + 2x) ^ 1 / 2 - (1 + 3x) ^ 1 / 3 (x - > 0) Expressed as a power function of X

Find the equivalent infinitesimal of (1 + 2x) ^ 1 / 2 - (1 + 3x) ^ 1 / 3 (x - > 0) Expressed as a power function of X

Let y [x] = (1 + 2x) ^ (1 / 2) - (1 + 3x) ^ (1 / 3),
Limit[y[x],x -> 0]=0,
Limit[y'[x],x -> 0]=0,
Limit[y''[x],x -> 0]=1,
so
Y [x] and 1 / 2 × x ^ 2 are equivalent infinitesimals
explain
If X - > 0, the function of order N-1 of Y [x] is 0, and the function of order n of Y [x] is m, (m ≠ 0), then
Y [x] and x ^ n × M / N! Are equivalent infinitesimals