EJERCICIOS

 

@E@RININJY @YXDHNYXNID IDQNXPLJ 0

B`rhnm`¸s B`rhnm `¸s Ifn Ifnig`m ig`m Cditjry Cditjry pjs pjs`` `` vdr vdrnds nds tn tn`mhd `mhds s `m `l är`d h`l Fnl Fnltjm tjm F`dh, Idrjlnmd h`l Yur. Dl `mtr`vnstdr d ljs idmhnhdtjs pdrd `l pu`stj h` o`s`rj, dl prjpn`tdrnj l` kustdrïd nmilunr nmcjrodinùm r`c`r`mt` d ld prjpnmd qu` um o`s`rj `sp`rd kdmdr pjr iu`mtd (j mjtd).prjpnmds Pm `stuhnj h` 011 `l o`s`rj kdmdbd lds snkun`mt`s pjr turmj h`iu`mtds 6 fjrds.r`in`mt`s nmhniù qu`

 D) ºIuäl `s ld prjbdbnlnhdh h` qu` umd prjpnmd s`d h` $211 j oäs: Y`d  x  `l  `l vdljr h` ld prjpnmd, `mtjmi`s5  p?

  x = $ 211   01 ?1.4 ? tjtdl h` prnpnmds prnpnmds jbs`rvdhds jbs`rvdhds 011

B) Lds idt`kjrïds $1 d $21, $21 d $01, `ti., s` ijmsnh`rdm outudo`mt` `xiluy`mt`s: ljs vdljr`s sjm tjodhjs `m iu`mtd `m um sjlj nmt`rvdlj, yd qu` `l lïont` sup`rnjr h` um nmt`rvdlj y `l lïont` nmc`rnjr h`l snkun`mt` nmt`rvdlj sjm ljs onsojs, `mtjmi`s ljs `v`mtjs h`cnmnhjs pjr hnifds idt`kjrïds sjm `v`mtjs outudo`mt` `xiluy`mt`s. I) Yn lds prjbdbnlnhdh`s r`ldinjmdhds ijm idhd r`sultdhj s` suodrdm, ºiuäl s`rïd `l tjtdl: @l tjtdl s`rïd 4 H) ºIuäl `s ld prjbdbnlnhdh h` qu` umd prjpnmd s`d h` $01:

 

Yn h`cnmnojs qu` `l vdljr h` $01 p`rt`m`i` dl nmt`rvdlj $01 d $411, `mtjmi`s5  p ( x ?01 )?

  ;0 011

?1.40

@) ºH` qu` umd prjpnmd s`d nmc`rnjr d $211: Y`d  x  `l  `l vdljr h` ld prjpnmd, `mtjmi`s5 ( < 211) ? 4 - ( = 211) ? 4 ’ 1.4 ? 1.>

00. @m um prjkrdod h` `opl`dhjs qu` r`dlnzdm präitnids h` k`r`mind `m Ildr`ojmt @mt`rprns`, 61% h` ljs `opl`dhjs sjm oue`r`s y 21% fjobr`s. >1% h` lds oue`r`s cu`rjm d ld umnv`rsnhdh y ;6% h` ljs fjobr`s cu`rjm d ld umnv`rsnhdh.  D) Dl dzdr s` `lnk` um `opl`dhj qu` r`dlnzd präitnids h` k`r`mind. ºIuäl `s ld prjbdbnlnhdh h` qu` ld p`rsjmd s`l`iinjmdhd s`d umd oue`r qu` mj dsnstnù d ld umnv`rsnhdh: Y`d  x  `l  `l `v`mtj h` `l`knr umd oue`r. Y`d y  `l  `l `v`mtj h` `l`knr d dlkun`m qu` mj cu` d ld umnv`rsnhdh. @mtjmi`s5 ()(y) ? (1.6) (1.4) ? 1.16

B) º@l kîm`rj y ld dsnst`mind d ld umnv`rsnhdh sjm nmh`p`mhn`mt`s:ºQjrquî: Mj sjm `v`mtjs nmh`p`mhn`mt`s hdhj qu` ljs hdtjs nmhnidm qu` fdy umd r`ldinùm `mtr` `l pjri`mtde` h` fjobr`s (;6%) y oue`r`s (>1%) qu` cu`rjm d ld umnv`rsnhdh. I) Ijmstruyd um hndkrdod h` ärbjl qu` ou`str` lds prjbdbnlnhdh`s ijmhninjmdl`s y prjbdbnlnhdh`s ijmeumtds.

 

YN PMNS@RYNHDH (1.;6) FJOBR@ MJ PMNS@RYNHDH

1.2

(1.22) K@M@RJ YN PMNS@RYNHDH 1.> OPE@R (1.6) MJ PMNS@RYNHDH (1.4)

H) Lds prjbdbnlnhdh`s ijmeumtds suodm 4.11 ºQjrquî: Lds prjbdbnlnh`s prjbdbnlnh`s ijmeumtds h`b`m suodr 4 yd qu` s` `mumindm tjhjs ljs pjsnbl pjsnbl`s `s r`sultdhjs. 32. Iudr`mtd pjr in`mtj h` lds idsds ijmstrunhds `m `l är`d h` Tudnl Ir``g nmiluy`m um snst`od h` s`kurnhdh. Y` s`l`iinjmdm 9 idsds dl dzdr.  D) ºIuäl `s ld prjbdbnlnhdh h` qu` lds tr`s idsds s`l`iinjmdhds iu`mt`m ijm snst`od h` s`kurnhdh: Y`d x `l `v`mtj h`cnmnhj pjr `l`knr umd idsd qu` nmiluy` um snst`od h` s`kurnhdh. @mtjmi`s5 ()()() ? (1.8)(1.8)(1.8) ? 1.138

B) ºH` qu` mnmkumd h` lds tr`s idsds s`l`iinjmdhds iu`mt` ijm snst`od h` s`kurnhdh: Y`d x `l `v`mtj h`cnmnhj pjr `l`knr umd idsd qu` mj nmiluy` um snst`od h` s`kurnhdh. @mtjmi`s5 ()()() ? (1.3)(1.3)(1.3) ? 1.243

I) ºH` qu` pjr lj o`mjs umd h` lds idsds s`l`iinjmdhds iu`mt` ijm snst`od h` s`kurnhdh:

 

Y`d x `l `v`mtj h`cnmnhj pjr `l`knr umd idsd qu` nmiluy` um snst`od h` s`kurnhdh. @mtjmi`s5 4 − ()()() ? 4 − (1.3)(1.3)(1.3) ? 4 − 1.243 ? 1.;68 H) ºYupjm` qu` ljs `v`mtjs sjm h`p`mhn`mt`s j nmh`p`mhn`mt`s:  R/ Yjm `v`mtjs nmh`p`mhn`mt`s. @E@RININJY IDQNXPLJ 3

81. @l k`r`mt` h` p`rsjmdl h` Iuob`rldmh Qnk Nrjm Ijopdmy `stuhnd `l mõo`rj h` diinh`mt`s ldbjrdl`s `m um o`s y `ldbjrù ld snkun`mt` hnstrnbuinùm h` prjbdbnlnhdh. Idliul` ld o`hnd, ld vdrndmzd y ld h`svndinùm `stämhdr h`l mõo`rj h` diinh`mt`s `m um o`s.

Muo`rj h`

Q ( x)

  x . Q ( x)

1

1. 8 1

1

1

1

1

4

1. 2 1

1.2 1

( - 1 .9 1 )

1 .1 >

1.1 46

2

1. 2 1

1.8 1

1.; 1

1 .8 >

1.1 >6

diinh`mt`s

〓 (  −) 〛〓] (  −)   〛〓 ]2(  −)  

 

 

@E@RININJ 08. Yupj Yu pjmk mkd d qu qu` ` Fd Fdin in`mh `mhd d `stu `stuhn hnd d ld id idt` t`kjr kjrïd ïd h` ld lds s ijm ijmtr trnb nbuin uinjm` jm`s s pd pdrd rd ld b`m`cni`mind. Y` s`l`iinjmù umd ou`strd h` 20 h`ildrdinjm`s h` pdr`eds eùv`m`s h` `mtr` 21 y 90 dôjs h` `hdh ijm um nmkr`sj brutj h` oäs h` $411 111. H` `stds 20 h`ildr h`ildrdinjm`s dinjm`s,, inmij nmiluïd nmiluïdm m ijmtrn ijmtrnbuinjm buinjm`s `s h` b`m`c b`m`cni`min ni`mind d h` oäs h` $4 11 111. 1. Yu Yupj pjmk mkd d qu` iudt iudtrj rj h` `s `std tds s h` h`il ildrd drdin injm jm`s `s s` s` s`l`i l`iin injmd jmdm m pdr pdrd d prditnidrl`s umd duhntjrïd ijopl`td.  D) @xplnqu` pjr quî r`sultd dh`iudhd ld hnstrnbuinùm fnp`rk`joîtrnid R/ Qjr quî s` trdtd h` umd pjbldinùm p`qu` p`qu`ôd ôd y cnmnt cnmntd, d, pjr tdmtj ld vdrndinùm h` ld prjbdbnlnhdh h` îxntj pu`h` s`r snkmncnidtnvd. B) ºIuäl `s ld prjbdbnlnhdh h` qu` `xditdo`mt` umd h` lds iudtrj h`ildrdinjm`s duhntdhds tuvn`rdm h`huiinjm`s h` b`m`cni`mind h` oäs h` $4 111:  Q ( x )?( sIx )( M − sIm− x ) (( MIm))

( ?4)?(0 I 4 )( 20 −0 I  8 −4 )? 1,8013 (( 20 I 8 ))

 Q  x

I) ºIuäl `s ld prjbdbnln prjbdbnlnhdh hdh h` qu` pjr lj o`mjs umd h` lds iudtrj h`ildr h`ildrdinjm`s dinjm`s duhntdhds tuvn`rdm h`huiinjm`s h` b`m`cni`mind h` oäs h` $4 111:

( ≠ 4) ? 4 - ( ? 1)

( ? 1 )?( 0 I 1 ) ( 20 −0 I  8 −1 )   ? 1,969 ( 20 I 8 )

 Q  x

(

 )

( ≠ 4) ? 4 - 1.969 ? 1.34;