RHPKOHC # 1 KÈCKWCJ DG QHPOH[ QHPOH@CG[
Presentado por:
Stiven David Zapata Castro
Mauricio Arcila Cano
Fredy Alberto Jaramillo
Cataño
Cálculo en Varias Variables 2303B04G1G2
Uniremington
2023
TGIH= KÈCKWCJ OLAOLOTG[OIHC _ IÏTJDJ[ LWIÏPOKJ[
8.[ghl () 9 ∦ 9 ,
h. J`tglfh (, ) dg ihlgrh gxhkth.
Kjij a ( x )9 cl x ∦ x 298,>
8
a ( x )9
8
8
⇐ a ( 8,> ) 9
9 2,7777777 …
x
8,>
`. J`tglfh (, ) dg ihlgrh hprjxoihdh phrh vhcjrgs dg ℌ 9 2,0, ℌ 9 2,2; ∦ ℌ 9 2,224
Rhrh n 92,0
a ( 8,> ) 9
8
a ( 8,> + 2,0 )∐ a ( 8,> ) cl
cl0
0 ∐cl8,>
9
92,701>2076>0> …
2,0
2,0
Gc grrjr rghc gs=
Grghc 9|2,7777777∐2,701>2076>0>|92.20>670?0860
Rhrh n 92,2;
a ( 8,> ) 9
8
a ( 8,> + 2,2; )∐ a (8,> ) cl8,>; ∐cl 8,
8,>
>
9
92.772?616;86
2,2;
2,2;
Gc grrjr rghc gs=
Grghc 9|2,7777777 ∐2,772?616;86|92.22476>61>;
Rhrh n 92.224
a ( 8,> ) 9
8
a ( 8,> + 2,224 ) ∐a (8,> ) cl 8,>
8,>24
24 ∐cl 8,>
8,>
9
92.22008?6716; …
2,224
2,0
Gc grrjr rghc gs=
Grghc 9|2,7777777 ∐2,22008?6716;|92.77;;;764;06
0. Rjr ajriuch dg ; pultjs rgsugcvh gc sofuogltg gmgrkokoj
Rhrh cjs dhtjs dg ch th`ch, glkugltrg a '0 a ''0
Wtocozhldj phrh ch proigrh dgrovhdh ch ajriuch=
8
U a ( x 2+ n ) ∐a ( x 2 ∐n ) Y
0n
Kjl n 92,7 sg toglg qug=
8
8
a ( 0 )9
U a ( 0 + 2,7 )∐ a ( 0 ∐2,7 ) Y 900,7 ∐?,7
0 ( 2,7 )
8
a ( 0 )98;
8
a ( x 2 ) ∐º
Wtocozhldj phrh ch sgfuldh dgrovhdh ch ajriuch=
a ( {x} rsu` {2} )9 {8} jvgr {{n} \ {0}} cgat Ua cgat ({x} rsu` {2} -n rofnt ) -0 a cgat ({x} rsu` {2} rofnt ) +a( {x} rsu` {
Pggipchzhldj cjs vhcjrgs kjljkodjs, sg toglg qug=
a ( 0 )9 {8} jvgr {{2,7} \ {0}} cgat Ua cgat (0 - 2,7 rofnt ) -0 a cgat (0 rofnt ) +a( 0 + 2,7 ) rofnt
a (0)9 {8} jvgr {2,07} cgat Ua cgat (8,7 rofnt ) -0 a cgat (0 rofnt ) +a( 0 ,7) rofnt
a (0)9 4 cgat U?,7 - 0(87) +0 0 ,7) rofnt Y 9
;. Pgfch dgc trhpgkoj
Rrjkgdoiogltj=
Dgtgriolhkojl
Dgtgriolhkojl dgc vhcjr dg n=
n9
8 ∐2
7
Cjs tïrioljs h suihr sjl=
a ( h )9 a ( 2 )9 8
0 a ( h + n )9 0 .
8
8 + 2,0
0 a ( h +0 n ) 90 .
0 a ( h + ; n ) 90 .
0
98 , ?0;8
8
0
98 , 6048
0
98 , 4621
0
98 , 08?7
8+ 2,4
8
8 + 2,1
0 a ( h + 4 n ) 90 .
8
8+ 2,>
0 a ( ` )9a ( 8 )9 2,7
Ch suih dg gstjs rgsucthdjs gs= 6,>;6;
Rjr cj thltj
8
∥ 8 +8x
2
0
8
≎ . 2,0 . 2,6>;6;92,6>4
0
Grrjr kjigtodj=
a (x)9 {0(; {x} \ {0} -8)} jvgr {(8+ {x} \ {0} {)} \ {;}
Pggipchzhldj
Pggipchzhl
dj cjs vhcjrgs rgspgktovjs sg toglg=
a ( 2 )9 {0(; {(2)} \ {0}
{ 0} -8)} jvgr {(8+ {(2)} \ {0} {)} \ {;}} 9a ( 8 )9 {0(; {( 8 )} \ {0} -8)} jvgr {(8+ {( 8 )} \ {0} {)} \ {;}} 9 {4} jvgr {>} 9 {8} jvgr {0
Gh 9 º
Jtrh ajrih dg khckuchr gc grrjr=
Gh 9 º
Gc vhcjr vgrdhdgrj dg ch oltgfrhc gs=
∐8
thl 8 92,6>7;?>81
Grrjr vgrdhdgrj= 2,22620781;