3.2 Resolucion de Ejercicios

 

>. Dk dkd`nhtd idk iamujl pdsn ?66 bg. y kn klhgatui idk mrnzl ilhid sd nplyn ds id 46 oe. Kn clreagn pdsn > g. ¼^uá klhgatui idmdrî tdhdr dk mrnzl ilhid sd nplyn kn clreagn pnrn plidr  kdvnhtnr nk dkd`nhtd< >º grnil (Ahtdrnplynhtd)

 Npkao @ 5 ?66 Bg

@ .i 5 ] . r 

] 5 >g

i 5 46 oe. r 5 ¼< r 5 >4666666 oe 5 >46 be

 

=. Kn onrrdtakkn dstî onrgnin olh 46 bg. id nrdhn. n. ¼^uá `udrzn cn cnmrî mrî qu qud d rdnkaznr pnrn kdvnhtnrkn< m. ¼^uá tapl id pnknhon ds< =º grnil (Ahtdrrdsastdhtd)

   N

M

O

Ylenhil eledhtl dh dk puhtl id nplyl pnrn dk dquakamral dstîtaol: @.i ‟ ].r 5 6 @5

¼<

@ .i 5 ] . r 

] 5 46 bg

i 5 >,1 e. r  5>e  

@ 5 =0,?> bg

 

?. ¼^uá `udrzn rdnkaznrî dk oakahirl cairîukaol id kn grún pnrn kdvnhtnr uh pdsl id >666 bg.< n. ¼^uá tapl id pnknhon ds< ?º grnil

@5

¼<

@ .i 5 ] . r 

] 5 >666 bg

i 5 >,4 e r5 4e @ 5 ????,? bg

 

A

9. ¼Ouîk sdrî kn vdkloaini id rltnoaÿh idk dhgrnhnjd olhiuoail dh kns saguadhtds  pnrdjns id dhgrnhnjds, I ?  y I 4   ) sa kn rudin eltraz garn n uhn vdkloaini  id >636 rpe. Onkouknr: n. Kn rdknoaÿh id trnhseasaÿh idk _astden > nk 0    m. Kn vdkloaini n kn qud garn kn plkdn 0 

 

plkdn =

 

I> 

a>-0 5

I=

4

   

a>-0

5 ---------- x

----------

?6

 H0

x ----------

5

----------

I0 

4

---------- x ----------

?6

 

x

I4 

I9 

4

?6

 

I? 

----------

 

plkdn 9

 H>

> 5

>

--------

x

>

------ x --------

0

0

> 5

------

0

=>0

]tn: dk _astden rdiuod kn vdkloaini id rltnoalh =>0 vdods

Id kn dounoaÿh (>):  H0

 

a>-0 5

----------

Dhtlhods:

H0 5

a>-0 x  H>

 H0 5

4 rpe

 H>  

(>)

5

>/=>0 x

>636

 

A

>9. @åjntd dh dk dxpraeailr id `rutn dk djd idk eltlr garn n >366 rpe. y kkdvn uh dhgrnh dhg rnhnj njd d N id >6 iadhtd iadhtds. s. Kn rudi( rudi(ZN ZN 5 >6). >6). _a Dk dh dhgrn grnhn hnjd jd N trnhs trnhseat eatd d dk elvaeadhtl nk dhgrnhnjd M qud tadhd 96 iadhtds, dh dk easel djd sd tadhd ltrl dhgrnhnjd O id >= iadhtds qud sd olhdotn n ltrl dhgrnhnjd id 06 iadhtds. ¼N qud vdkloaini garn dk onmdznk idk dxpraeailr (HI)

Z   N 5 >6

Z M 5 96

 

 

Z O O   5 >= Z I 5 06 y

ZN 

a>-0 5

ZM

 

>

 

a>-0

   

----------

>366 rpe

 HI 5

----------

ZI

x

9

 

 

x

5

>6 5

 HN

----------

>= x

96

>

5 ----------

 

Z O 

----------

 

H   N

---------

5

> / =6

4

HI

a>-0

5

--------------

DHYLHOD_:

 HI  5 >/=6 x >366 ]VE

 HN  HI 5 16 rpe

--------

06

 

A

0.- Kn `agurn rdprdsdhtn uh eltlr qud cnod garnr uh tlrhakkl sah`åh, qud n su vdz cnod garnr n uh dhgrnhnjd. Kn plkdn qud vn elhtnin slmrd dk djd id iaocl dhgrnhnjd (vdrid) tadhd uh iaîedtrl id 0 oe y kn plkdn qud dstî elhtnin slmrd dk djd id snkain (rljl) tadhd uh iaîedtrl id ?6 oe. _a dk eltlr garn n >466 rpe. ¼Ouîhtls iadhtds tdhirån qud tdhdr dk dhgrnhnjd (=) pnrn qud dk djd id snkain garnsd n =4 rpe< ¼Ounk ds kn rdknoalh id trnhseassalh idk _astden<

 

DHG]NHNJD (=)

 

VLKDN OLHITOYL]N (?)

 

VLKDN OLHITOAIN (9)

YL]HAKKL _AH@AH (>)

 

ELYL] DKDOY]AOL

 

Z> 

 

a>-0 5

----------

 

 

---------Z=

 

Z=

 

>

a>-0

5

----------

0 

----------

 H9 5

----------

I9

>

 

 

x

Z=

 

 

I? 

---------

96

--------------

>466 rpe

>=

0 x

----------

=4 rpe 5

?6

5

5

 H>

0 x

>6

---------

?6

> 5

-------------------------- -

?6

5

>/?6

>= x

--------

06

 

A

v dkloaini idk eltlr elt lr ds id =666 rpe y dk húedrl id iadhtds iadhtd s id 7.- _a kn vdkloaini kls dhgrnhnjds ds dk id kn `agurn. Onkoukn kn vdkloaini id garl idk îrmlk AAA, dh kls saguadhtds onsls: n) Dhgrnhnh >-= y 4-0 4-0 m) Dhgrnhnh ?-9 y 7-3.

n) Dhgrnhnh >-= y 4-0

 

 

Z> 

a>-3 5

Z4 

----------

x

Z=

 

5

Z0

06

----------

x

0

--------

46

5 ----------- 5 >.=

?6

4

 H0

 

 

----------

?6

a>-0

5

>.=  5

---------

Dhtlhods:

 H0

5

=966 rpe 

=666 7-3. m) Dhgrnhnh ?-9 y 7-3.

 

Z? 

a>-3 5

----------

Z9 

 

Z7  x

----------

Z3

46 5

----------

=6 x

--------

?6

5

6.970=

76

 H0

 

a>-0

5

6.970=  5

---------

=666

Dhtlhods:

 H0

5

14=.9 rpe 

 

A

>6.  Dk trdh id dhgrnhnjds id kn `agurn, tadhd kns saguadhtds rdknoalhds id >6.  trnhseassalh dhtrd djds aA-AA 5 >/=, aAA-AAA 5 >/?, aAAA-AP 5 >/4. n) Iamujn dk pdr`ak idk _astden. m). Onkoukn dk húedrl id rdvlkuoalhds olh qud garn dk îrmlk AP sa dk îrmlk eltraz garn n >=66 rpe. o) Idtdreahnr dk húedrl id iadhtds id tlils kls dhgrnhnjds id elil qud dh hahgúh onsl kls dhgrnhnjds tdhgn edhlr id >= iadhtds ha enylr id 06 iadhtds.

 

>

=

n)

?

9

4

0

 

 

A

m)

 

Z> 

a>-0 5

----------

Z=

 

> 

   

Z? 

a>-0

5 ---------- x

=

x

----------

Z4  x ----------

Z 9 

> ?

5

----------

Z0 

>

---------- x ----------

 H0  H>

> 5

4

(>)

--------

H0 5

?6

 

---------

>=66 rpe

H0 5 96 rpe

o)   >   

 

a>-0

5 ---------- x

=

Dhtlhods:

Z> 5 >=

 

Z= 5 =9

 

Z? 5 >=

 

Z9 5 ?0

 

Z4 5 >=

 

Z0 5 06

>

>

---------- x ----------

?

4

>= 5

--------

=9

>= x

---------

?0

>= x --------

06

 

A

>>. Iasdþnr uh trdh id dhgrnhnjds ilhid dk uktael dhgrnhnjd idmd tdhdr uhn vdkloaini id rltnoalh id =6 rpe y dk eltlr dkdotrao sueahstrn =966 rpe id vdkloaini id garl. Dh haguh onsl dk húedrl id iadhtds idk dhgrnhnjd idmd sdr edhlr id >=, ha enylr id 7=. (Kn rdspudstn olrrdotn ds ounhil dk húedrl id pnrnds id dhgrnhjd sdkdooalhnil sdn kl eåhael)

   

Z> 

a>-0 5

---------Z=

Z?  x

---------Z 9 

Z4  x ---------Z0 

 H0 5

--------- H>

(>)