Algèbre, Arithmétique et Géométrie. Classe de Troisième by C.; Hemery, C. Lebosse PDF

By C.; Hemery, C. Lebosse

Cours conforme au programme du 23 juin 1962.

Table des matières :

Algèbre et Arithmétique

Leçon 1 — Rapports
Leçon 2 — Proportions
Leçon three — Racine carrée entière d’un nombre entier
Leçon four — Racine carré approchée. — Racine carrée exacte
Leçon five — Radicaux arithmétiques. — Racines d’un nombre relatif
Leçon 6 — Expressions algébriques. — Monômes
Leçon 7 — Polynômes
Leçon eight — Multiplication des monômes et des polynômes
Leçon nine — Identités remarquables
Leçon 10 ­— department des monômes et des polynômes. — Décomposition en facteurs
Leçon eleven — Fractions rationnelles
Leçon 12 — Équation du finest degré à une inconnue
Leçon thirteen — Équations qui se ramènent au most suitable degré. — Équations littérales
Leçon 14 — Systèmes d’équations du best degré
    Élimination par substitution
    Élimination par addition
    Généralisations
Leçon 15 — Inéquation du premiere degré à une inconnue
Leçon sixteen — Les problèmes d’algèbre
Leçon 17 — Fonctions et graphiques
Leçon 18 — Étude de los angeles fonction : y = ax
Leçon 19 — Étude de l. a. fonction : y = ax + b
Leçon 20 — functions de l. a. fonction : y = ax + b

Géométrie

I. Géométrie plane

Leçon 1 — Rapport de deux segments. — issues divisant un section dans un rapport donné
Leçon 2 — Théorème de Thalès
Leçon three — purposes du théorème de Thalès
    Propriété des bissectrices d’un triangle
    Constructions
Leçon four — Triangles semblables
    Premières applications
Leçon five — Cas de similitude des triangles
Leçon 6 — functions de l. a. similitude
Leçon 7 — family métriques dans le triangle rectangle
Leçon eight — Rapports trigonométriques
Leçon nine — family trigonométriques dans le triangle rectangle
Leçon 10 — kinfolk métriques dans le cercle
Leçon eleven — structures géométriques
Leçon 12 — Polygones réguliers. — Périmètre du cercle
Leçon thirteen — Mesure des aires

II. Géométrie dans l’espace

Leçon 14 — Généralités sur le plan
Leçon 15 — Droites parallèles. — attitude de deux droites
Leçon sixteen — Droite et plan parallèles
Leçon 17 — Plans parallèles
Leçon 18 — Droite et plan perpendiculaires
Leçon 19 — Droites orthogonales. — Perpendiculaires et obliques
Leçon 20 — Angles dièdres
Leçon 21 — Plans perpendiculaires
Leçon 22 — Projections orthogonales. — Vecteurs

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Additional info for Algèbre, Arithmétique et Géométrie. Classe de Troisième

Example text

Let / g C\a, ft], and let p be in the open interval (a, ft). a. Suppose f{p) ^ 0. Show that a 5 > 0 exists with /(x) ^ 0, for all x in [/? — 5, /? + 5], with fp — (5, p + <5] a subset of [a, ft], b. Suppose /(p) = 0 and ft > 0 is given. Show that a 5 > 0 exists with |/(x)| < ft, for all x in [p — (5, p + >5], with [p — 5, p + 3] a subset of [a, ft]. DISCUSSION QUESTION 1. 2 In your own words, describe the Lipschitz condition. Give several examples of functions that satisfy this condition or give several examples of functions that do not satisfy this condition.

A. Show that for all x > 0, /(x) = x — sinx is nondecreasing, which implies that sinx < x with equality only when x = 0. b. Use the fact that the sine function is odd to reach the conclusion. A function / : [a, ft] —IR is said to satisfy a Lipschitz condition with Lipschitz constant L on [a, ft] if, for every x, y G [a, ft], we have |/(x) — /(y)| < L|x — y|. a. Show that if / satisfies a Lipschitz condition with Lipschitz constant L on an interval [a, ft], then / € C[a, ft]. b. Show that if / has a derivative that is bounded on [a, ft] by L, then / satisfies a Lipschitz condition with Lipschitz constant L on [a, ft].

I-TUV3 liy 20 d. 4 5 • V3 1 3 + 11/ 20 6. Use three-digit rounding arithmetic to perform the following calculations. Compute the absolute error and relative error with the exact value determined to at least five digits. a. 921 b. 499 c. 327) - 119 d. 327 7. Use three-digit rounding arithmetic to perform the following calculations. Compute the absolute error and relative error with the exact value determined to at least five digits. U_ 6 3 _li Z_ b. 4 62 c 8. iivm d. V W ' V\3-VJ\ Repeat Exercise 7 using four-digit rounding arithmetic.

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Algèbre, Arithmétique et Géométrie. Classe de Troisième by C.; Hemery, C. Lebosse


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