Exercicios Resolvidos Capitulo 5 Retas Paulo Winterle. Uploaded by. Filipe Ascenção. connect to download. Get pdf. 15 ago. dos vetores no Cálculo. FEITOSA, M. O: Cálculo Vetorial e Geometria Analítica: exercícios propostos e resolvidos, 4ª edição, São Paulo. Mecanica Vetorial Exercicios Resolvidos Mecanicaclassica Calculo Vetorial · Calculo Vetorial I Cap. 1. calculo vetorial e geometria analítica.

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In Examples 2 and 3, the number 0 is the minimum element. Find the area of the triangle formed by the points 1, 2 exercicils, 3, 4 and 5, 0. It follows that T must have a smallest member, and in turn this proves that the well-ordering principle is a consequence of the principle of induction.

There is a very useful and convenient notation which enables us to Write sums like this in a more compact form. The set P of positive integers 1, 2, 3. Since Tisnonempty, there is a positive integer t in T. Axiom 10 allows us to introduce irrational numbers in the real-number system, and it gives the real-number system a property of continuity that is a keystone in the logical calculo vetorial e geometria analitica exercicios resolvidos of calculus.

A proof of this statement is outlined in Exercise 11 of Section 1 3. Since P is nonempty, Axiom 10 tells us that P has a least Upper bound, say b.


Let S be the set of a11 positive real numbers. Definitions of the terms lower bound, bounded below, smallest member or minimum element may be similarly formulated. Assume P is bounded above.

The Archimedean property of the real-number system 2 5 In a11 these examples it was easy to decide whether or not the set S was bounded above or below, and it was also geometrix to determine the numbers sup S and inf S.

The next example shows that it may be difficult to determine whether Upper or lower bounds exist. In Example 1, the set of a11 positive real numbers, the number 0 is the infimum calculo vetorial e geometria analitica exercicios resolvidos S. Of course, it is not important that we use the letter k; any other convenient letter may take its place. Axiom 10 tells us that there is a number B which is a supremum for -S.

For example, we havl: Let n and d denote integers. Calculo vetorial e geometria analitica exercicios resolvidos Axiom 10, we cari prove the following. The infimum exercidios S, when it exists, is uniquely determined and we denote it by inf S.

Exercicios Calculo Vetorial

Enviado por Danilo flag Denunciar. The integer 1 cannot be in T otherwise it would be the smallest member of T. A set with no Upper bound is said to be unbounded above.

The reader should formulate these for himself. If S has a maximum element, this maximum is also a least Upper bound for S. This is ana,itica the set in Example 2 except that the point 1. Thus a11 four have blue eyes. Post on Oct views.


Exercicios Calculo Vetorial – [PDF Document]

It is an important number in calculus called the Euler number e. But this t must also be in S since S contains a11 positive integers. This set is bounded above by 1 but it has no maximum element.

There cari be at most one such B.

In Example 3 above, the number 1 is a least Upper bound for T although T has no maximum element. First, pick a point on the line, e. Enviado por Danilo flag Denunciar. The nota t ion in 1. Then Sis said to be bounded above by B.

Exercicios Resolvidos Capitulo 5 Retas Paulo Winterle | Filipe Ascenção –

Prove the fo l lowing s ta tement by induct ion: There is another axiom of fundamental importance in calculus that is ordinarily not discussed in elementary algebra courses.

This example is from G. Irrational numbers arise in elementary algebra when we try to salve certain quadratic equations. It has no upper bounds and it has no maximum element.