Can the formulas such as tanx-sinx, tanx-x and sinx-x be used directly?

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The expression of your question is not very rigorous, for example, those are not formulas, but infinitesimal substitutions. Moreover, your statement is ambiguous-except that people generally think that you are asking if you can use sinx directly.

replace

tanx，

There are also a few people who like to buckle words as much as I do. They may understand that you are asking if you can use x-tan for sinx-tanx (minus sign is not tilde).

X or something The following answers are based on the first understanding.

It can be used, and it is suggested that constant deformation and equivalent infinitesimal substitution should be given priority when seeking the limit.

Other related discussions:

1.

Replacing x with f(x) can be similar as long as the condition is met (that is, f(x) tends to zero). For example, with

commit a crime

f(x)

Substitute tan

f(x)；

2.

Generally, it is the equivalent substitution of product factor, and the addition and subtraction factors in the sum-difference formula cannot be replaced separately, as someone said upstairs;

3.

This kind of equivalent substitution is transitive, that is, A can replace B, B can replace C, and C can replace A. ..