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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If a line of unit length is given, then a line of length calculo vetorial e geometria analitica exercicios resolvidos cari be constructed with straightedge and compass for each positive integer n. In a later chapter we Will learn that sup S is an irrational number approximately equal to 2. Of course, it is not important that we use the letter k; any other convenient letter may take its place.

TO emphasize once more that the choice of dummy index is unimportant, we note that the last sum may also be written in each of the following forms: Enviado por Danilo flag Denunciar. In this case it is not easy to determine the value of sup S from the description of S. Using the inner product to prove the converse of the Pythagorean theorem: First, find two sides of the triangle.

Let S be the set of a11 positive real numbers. Compute n,and prove tha t the inequal i ty i s calculo vetorial e geometria analitica exercicios resolvidos rue for a11 in tegers n 2 n1. The above relation can be remembered by a cyclical permutation of i, j,k.

It has no upper bounds and it has no maximum element. Other uses of the summation notation are illustrated below: This is called the least Upper bound of the set and it is defined as follows: A set with no Upper bound is said to be unbounded above.

## Apostol – Calculus Volume 1.pdf

Before we describe Axiom 10, it is convenient to introduce some more terminology and notation. But this t must also be in S since S contains a11 positive integers. The other identities are proved similarly. Using summation notation, we cari Write the sum in 1. There is a very useful and convenient notation which enables us to Write sums like this in a more compact form. We emphasize once more that the supremum of S need not be a calculo vetorial e geometria analitica exercicios resolvidos of S.

This is like the set in Example 2 except that the point 1. If S has a maximum element, this maximum is also a least Upper bound for S.

More generally, when we want to form the sum of several real numbers, say a,a. Enviado por Danilo flag Denunciar. Therefore, the assumption that T has no smallest member leads to a contradiction. The set S is also bounded above, although this fact is not as easy to prove. The Archimedean property of the real-number system 2 5 We shall show that this leads to a contradiction. For example, we havl: Axiom 10 tells us that there is calculo vetorial e geometria analitica exercicios resolvidos number B which is a supremum for -S.

There cari exerciciow at most one such B. Then Sis said to be bounded above rseolvidos B. If at least one of the g i r l s has b lue eyesthen a11 n of them have blue eyes. This set is unbounded above. It is common practice to refer to the least Upper bound of a set by calculo vetorial e geometria analitica exercicios resolvidos more concise term supremum, abbreviated sup.

In Examples 2 and 3, the number 0 is the minimum element. Find the numerical values of the fo l lowing sums: Since Tisnonempty, there is a positive integer t in T.

### Exercicios Resolvidos Capitulo 5 Retas Paulo Winterle | Filipe Ascenção –

Let T be a nonempty collection of positive integers. The integer 1 cannot be in T otherwise it would be the smallest member of T. Then determine the points of intersection of the line with the coordinate planes.

Home Documents Exercicios Calculo Vetorial. The reader should not ice tha t d nition by induction and proof by induction i nvo lve the same under ly ing idea. Let b denote a fixed positive integer.

This does calculo vetorial e geometria analitica exercicios resolvidos mean that one should not make use of geometry in studying properties of real numbers. Let S be the set of a11 real x satisfying 0 5 x 5 1. Once we know that S is bounded above, Axiom 10 tells us that there is a number which is the supremum of S. Thus a11 four have blue eyes. First, pick a point on the line, e. First, find two vectors in the plane.