Substitution of infinitesimal factors of higher number equivalence How do ^ 2 + (SiNx) ~ (sin2) / (SiNx) ~ (SiNx) ~ (sin2) ~ (SiNx) ~ (SiNx) ~ (SiNx) ~ (sin2) ~ (SiNx) ~ (SiNx) ~ (SiNx) ~ (SiNx) ~ (SiNx) ~ (SiNx) ~ (SiNx) ~ (SiNx) ~

Substitution of infinitesimal factors of higher number equivalence How do ^ 2 + (SiNx) ~ (sin2) / (SiNx) ~ (SiNx) ~ (sin2) ~ (SiNx) ~ (SiNx) ~ (SiNx) ~ (sin2) ~ (SiNx) ~ (SiNx) ~ (SiNx) ~ (SiNx) ~ (SiNx) ~ (SiNx) ~ (SiNx) ~ (SiNx) ~

How to eliminate the denominator? --- this is not to eliminate the denominator, but to find the limit, 1 + (SiNx) ^ 2 (SiNx) ^ 2 is infinitesimal, but 1 is not infinitesimal, omitting it does not affect the limit value, so (SiNx) ^ 2 is omitted. Or 1 is replaced by 1 + (SiNx) ^ 2

How to determine the equivalent infinitesimal factor of an advanced number problem?
Many topics on higher numbers need to use the equivalent infinitesimal factors to exchange, so how to determine the order of these factors and formulas? For example, 1-cosx, a ^ X-1, x ^ X-1, arcsinx, what are these equivalent infinitesimal factors?

The judgment should be very detailed
For example, we need to judge the infinitesimal order of F (x). That is to say, when X - > and f (x) / x ^ a limit exists, then f (x) and x ^ a have the same order
Of course, Taylor expansion can clearly see, but there is no need to do so troublesome
This is the most basic way to judge, you can also see through some other specific ways
For example, X and SiNx are of the same order, and many others are similar
It should be noted that the order of infinitesimal (x - > 0) is different from that of infinity (x - > infinity)
It's easy to ask these questions, so you can do it yourself

If the solution set of inequality ax-b > 0 about X is an open interval from one to positive infinity, then the solution set of inequality ax-b / X-2 > 0 about X is an open interval

Using the scalar root method, the two roots of the equation ax-b / X-2 = 0 are 1 and 2 respectively, so the solution set is x2