F (x) is the fifth order infinitesimal of X?

F (x) is the fifth order infinitesimal of X?

It means Lim X - > 0 f (x) / (x ^ 5) = 0
A beginner's question

When finding x →∞, √ [x + √ (x + √ x)], √ (1 + x) - √ (1-x) are infinitesimals of several orders of X respectively

Infinitesimal is a variable whose limit is the number of zeros. Therefore, it is obvious that only when x → 0, the latter two formulas really tend to 0. The following website is the definition of higher-order infinitesimal
In the first question, X is obviously a non negative number under the root sign. If you divide it directly by the 1 / 8 power of the smallest degree x, you can get the limit of 1, so it is the infinitesimal of order 1 / 8 of X;
In the second problem, multiply and divide by) √ (1 + x) + √ (1-x) at the same time, the molecule becomes 2x, and the denominator is 2 in the case of X → 0, so the formula becomes x, which is the first order infinitesimal of X and also the equivalent infinitesimal

1 + x ^ 2-e ^ x ^ 2 when x approaches 0, is the infinitesimal of order x

Fourth order