Can high order infinitesimal do four operations?

Can high order infinitesimal do four operations?


Can multiply and divide, can't add and subtract!
sinx^2/x^2
=x^2/x^2
=1



Infinitesimal operation
prove:
1 o(x^2)+o(x^3)=o(x^2)
2 x·o(x^2)=o(x^3)
It's understood by definition, but I can't understand it





Higher order infinitesimal problem
If a = x ^ m is a higher order infinitesimal of B = x ^ n, then M > n or m


A = x ^ m is the higher order infinitesimal of B = x ^ n, m 〉 n

Elden Ring Premiere

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