Let's ask a limit problem. If a (x) is an infinitesimal of higher order of X, then when x approaches zero, a (x) / x = 0, and a (x) * x / x = 0, right?

Let's ask a limit problem. If a (x) is an infinitesimal of higher order of X, then when x approaches zero, a (x) / x = 0, and a (x) * x / x = 0, right?

No, X divided by X. not equal to 0

Is higher order infinitesimal derivative or higher order infinitesimal
When proving that the Peano remainder R n (x) = O ((x-x0) * n) in Taylor formula, R n (x0) is still the same

The answer upstairs is really baffling and harmful
Y = x ^ 2 is the second order infinitesimal of X, and y '= 2x is the same order infinitesimal of X
Y = x is the equivalent infinitesimal of X, y '= 1 is not infinitesimal

What is the difference between infinitesimal and infinitesimal?

In fact, there is no difference between infinitesimal and infinitesimal
Similarly, infinity is referred to as infinity
The above statement is not right. They are all variables, the essence is the same