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Differentiation
| Content Provider | Scilit |
|---|---|
| Author | Kumar, Ajit Kumaresan, S. |
| Copyright Year | 2014 |
| Description | The basic idea of differential calculus (as perceived by modern mathematics) is to approximate (at a point) a given function by an affine (linear) function (or a first-degree polynomial). Let J be an interval and c ∈ J . Let f : J → R be given. We wish to approximate f(x) for x near c by a polynomial of the form a + b(x − c). To keep the notation simple, let us assume c = 0. What is meant by approximation? If E(x) := f(x) − a − bx is the error by taking the value of f(x) as a + bx near 0, what we want is that the error goes to zero much faster than x goes to zero. As we have seen earlier this means that limx→0 f(x)−a−bx x = 0. Book Name: A Course in Real Analysis |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2013-0-19684-5&isbn=9780429156526&doi=10.1201/b16440-9&format=pdf |
| Ending Page | 172 |
| Page Count | 44 |
| Starting Page | 129 |
| DOI | 10.1201/b16440-9 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2014-01-10 |
| Access Restriction | Open |
| Subject Keyword | Book Name: A Course in Real Analysis History and Philosophy of Science Function Mathematics Basic Taking Notation Want Keep Faster Earlier |
| Content Type | Text |
| Resource Type | Chapter |
