Imprecision and Uncertainty in Information Representation and Processing by Plamen Angelov & Sotir Sotirov

Author:Plamen Angelov & Sotir Sotirov
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

2.

3.

4.If and then

Proof

From the definition of the derivative and from the properties of the limit of functions it holds

1.

2. The proof of the second property is similar like the proof of the point 1.

3.

4. Let and then

Remark 3

Let for each there exist then it holds

5 Lagrange Mean Value Theorem

Our main aim is to proof the Taylor’s theorem. Of course before we do this we need to prove some more theorems. Lagrange mean value theorem is one of them. The results which are mentioned in this section were published in the paper [8].

Theorem 6

Let be continuous on [A, B] and differentiable on (A, B). Then there exists such that

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