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2.2. Equivalence of infinitesimal

Lecture



Let be   2.2.  Equivalence of infinitesimal and   2.2.  Equivalence of infinitesimal - infinitely small with   2.2.  Equivalence of infinitesimal .

If a   2.2.  Equivalence of infinitesimal then   2.2.  Equivalence of infinitesimal is infinitely small of a higher order compared to   2.2.  Equivalence of infinitesimal . In this case, it is said that   2.2.  Equivalence of infinitesimal there is " about small" from   2.2.  Equivalence of infinitesimal and write down:   2.2.  Equivalence of infinitesimal .

If a   2.2.  Equivalence of infinitesimal where k is a non-zero number, then   2.2.  Equivalence of infinitesimal and   2.2.  Equivalence of infinitesimal - infinitely small one order . In this case, it is said that   2.2.  Equivalence of infinitesimal there is " Oh big" from   2.2.  Equivalence of infinitesimal and write down:   2.2.  Equivalence of infinitesimal .

In the particular case, if   2.2.  Equivalence of infinitesimal then infinitesimal   2.2.  Equivalence of infinitesimal and   2.2.  Equivalence of infinitesimal called equivalent and write:   2.2.  Equivalence of infinitesimal ~   2.2.  Equivalence of infinitesimal .

If a   2.2.  Equivalence of infinitesimal then   2.2.  Equivalence of infinitesimal . Consequently,   2.2.  Equivalence of infinitesimal is infinitely small of a higher order compared to   2.2.  Equivalence of infinitesimal (   2.2.  Equivalence of infinitesimal ).

In calculating the limits, the following infinitesimal equivalence is often used:   2.2.  Equivalence of infinitesimal


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Mathematical analysis. Differential calculus

Terms: Mathematical analysis. Differential calculus