Ẓeṛ aɣbalu n Talast (Tusnakt)


Deg [[Tasleṭ|Tasleṭ tusnakt]], tazmilt n talast teglem tamawaẓt n wazalen n [[Asartu|usartu]] ma d amatar yettruḥu-d s ifeḍ, neɣ d [[Tasɣent (tusnakt)|tesɣunt]] ma d [[Amutti|umutti]]  yettaẓ-d ar waggaz ( yezmer lḥal d yifeḍ ) deg yiri n tɣult n tbadut. ma talast-nni tella deg  tegrumma n waggwaḍ, ihi ad nini d akken asartu neɣ tasɣunt yettaweḍ ( deg waggaz yettwaɣren ) . ma yella mačči akka, ihi d tamhelwayt am wakken yella deg isurta neɣ tisɣunin [[Tawulant|tiwulanin]] mačči timezgatin ( am tasɣunt [[sinus]] deg <math>+\infin</math> )

ddaw tawtilt n tilin, Akti n talast ad yili s usiḍen gar iferdisen s timhalin tiferdisin, ama nesɛa aṭas n telɣiwin tuffirin i zemren ad ilin. Asnemhel n  tigmi yettaǧǧa mennaw n tikwal ad tekkes tuffrawin-igi.

Aguccel d talast yezmer ad yifsus s tenfalit n ugdazal (ladɣa deg waddad n talast tilemt neɣ tifeḍt ), deg tanasaẓt tamezlagut neɣ deg ifurken  iknuziraren, neɣ taneflit yeffuken neɣ d anasaẓ.

== Talast n usartu ==

=== Imedyaten imezwura s isurta ilawen ===
ma <math>n</math> d amḍan ameqqran aṭas (ummid), imitti-ines <math>\frac{1}{n}</math> yuẓan aṭas ar 0. wagi nezmer ad negg s tugda yagi : <math>\lim_{n\to\infty} \frac 1n = 0</math>.



Am wakken, nezmer ad naru <math>\lim_{n\to\infty} \sqrt n = +\infty</math>, imi aẓar amkuẓ yezmer ad yili meqqer mliḥ ma ara d yili <math>n</math> meqqar akken iwata (amedya, akken ad nesɛu  <math>\sqrt n > 1000</math>, ilaq ad yili {{mvar|''n''}} > {{formatnum:1000000}} ) 


seg tama nniḍen, ur telli ara talast n usartu awalan <math>((-1)^n)_{n\in\N}</math>, iwumi ara ad yesɛu s temlellayt azalen 1 d -1, ama ur yettruḥu ara la ar -1 la ar 1, la ar wazal deg uzilal ]-1,1[ neɣ berra-s. imi yella d asartu ugmir, ihi ur yezmir ara ad yruḥ ar <math>+\infty</math> neɣ <math>-\infty</math>

=== Agtalɣa ===

==== talast ifuken ====
tabadut sɣur [[:fr:Weierstrass|Weierstrass]] n uggwaḍ n usartu ilaw <math>(x_n)_{n\in\N}</math> ar talast ifuken L<math>L\in\R</math> ad nfali s tenfalit agi : 

: <math>\forall \varepsilon>0\quad\exists n_0 \in \N\quad\forall n \geq n_0\quad L-\varepsilon < x_n < L+\varepsilon</math>

neɣ ugar, s tenfalit tagdazalt deg waddad n usartu ilaw, iwumi ara ad yezgu mliḥ deg isurta n wazalen isalalen.

: <math>\forall \varepsilon>0\quad\exists n_0 \in \N\quad\forall n \geq n_0\quad L-\varepsilon < x_n < L+\varepsilon</math>

tabadut agi ad ssiɣzef daɣen ar isurta deg tallunt tamawayt talugant s ubeddel n wazal amagdaz s walugen, arnu s umata ar isurta deg tallunt timizrirt s tenfalit agi : 

: <math>\forall \varepsilon>0\quad\exists n_0 \in \N \quad\forall n \geq n_0\quad \mathrm d(x_n, L) < \varepsilon</math>

deg sin addaden-igi, ur yezmir ara ad illin sin n tlasin i yemgaraden ar yiwen usartu, wagi aɣ-yeǧǧ ad negg tagda yagi :  <math>\lim_{n\to\infty}x_n = L</math>, nettaf tikwal tira yagi <math>x_n \underset{n\to\infty}{\longrightarrow} L</math> 

==== talast timifeḍt ====
neqqar d akken usartu <math>(x_n)_{n\in\N}</math> yettemhelway ar <math>+\infty</math> deg waddad agi: 



<math>\lim_{n\to\infty}x_n = +\infty \iff \forall M\in\R\quad\exists n_0 \in \N \quad\forall n \geq n_0\quad x_n > M</math>

S terwest, yettemhelway ar <math>-\infty</math> deg waddad agi : 



<math>\lim_{n\to\infty}x_n = -\infty \iff \forall M\in\R\quad\exists n_0 \in \N\quad\forall n \geq n_0\quad x_n < M</math>

== Talast n tesɣunt ==
tazmilt n talast n tesɣunt tettemcabi ar tazmilt n talast n usartu, siwa aya amutti n tesɣunt yezmer ad iruḥ ar wazal menwala deg taɣult n tbadut neɣ deg tilisa-ines.

daɣen, i yal tesɣunt tettwabadu deg yiwen uzilal <math>]a,b[ \subset \R</math>, nezmer ad nẓer talasin i zemrent ad ilint n tesɣunt deg yal ilaw  <math>c
</math> deg uzilal, ama daɣen deg yigmiren <math>a
</math> d <math>b
</math>, igmiren-a zemren ad ilin ifuken neɣ xaṭi. 

=== Talast ifuken seg wazal ifuken ===

==== Tabadut ====
i yal tasɣunt tilawt neɣ tasemlalt n yiwen umutti ilaw neɣ asemlal, tanfalit n talast ifuken deg wazal ifuken tettemcaba

ar tinna n talast n usartu  

: <math>\lim_{x\to a} f(x) = L \iff\quad\forall \varepsilon \in \R_+^*\quad\exists \delta \in \R_+^*\quad\forall x \in \mathcal D_f\quad(|{x - a}| < \delta \Rightarrow |f(x)-L|<\varepsilon)</math>

Tella daɣen : 



<math>\lim_{{x\to a}\atop{x \neq a}} f(x) = L \iff\quad\forall \varepsilon \in \R_+^*\quad\exists \delta \in \R_+^*\quad\forall x \in \mathcal D_f\setminus{\{a\}}\quad(|{x - a}| < \delta \Rightarrow |f(x)-L|<\varepsilon)</math>

=== talast deg uyeffus neɣ d uzelmaḍ ===
[[Tugna:Hyperbole_1_sur_x.png|alt=Représentation graphique de la fonction inverse|vignette|talasin deg yigrimiren n uzilal n tesɣunt timittit: <math>\lim_{x\to-\infty}\tfrac 1x=\lim_{x\to+\infty}\tfrac 1x=0</math>, <math>\lim_{x\to 0^-}\tfrac 1x=-\infty</math>, <math>\lim_{x\to 0^+}\tfrac 1x=+\infty</math>]]


talast n tesɣunt f ar uẓelmaḍ deg ilaw a yettwaru <math>\lim_{x\to a\atop x<a} f(x)</math> neɣ <math>\lim_{x\to a^-} f(x)</math>

akken , <math>f(a^-)</math> 

deg a yettwaru <math>\lim_{x\to a\atop x>a} f(x)</math> neɣ<math>\lim_{x\to a+} f(x)</math>

akken, <math>f(a^+)</math>

:

=== Imedyaten ===

* Talast n x-> 1/x deg ifeḍ yegda-d ar 0 : <math>\lim_{x\to \infty} \frac{1}{x} = 0</math>
* talast n x-> 1/x deg 0 ur telli ar. Talast teyeffust d ifeḍ <math>+ \infty</math> : <math>\lim_{x\to 0+} \frac{1}{x} = +\infty</math>  <math>\lim_{x\to 0-} \frac{1}{x} = -\infty</math>


[[Taggayt:Tusnakt]]
[[Taggayt:Tasɣunt]]
[[Taggayt:Tasleṭ]]