UNIVERSIDAD NACIONAL HERMILIO VALDIZAN FACULT FACULTAD AD DE INGENIERIA INGENIER IA CIVIL Y ARQUITECTURA ESCUELA ACADEMICO ACADEMICO PROFESIONAL DE INGENIERIA CIVIL PRACTICA 1.- El númer !e "#$% &r '(m#l#( en )n( !e*erm#n(!( re+#,n e% )n( (r#(le (le(*r#( / 0)( ')n0#,n !e &r(#l#!(! e%2
f 3 x 4 = P 3 X = x 4 = c
x 9
5 67158595:5;
(4 C(l0)l C(l0)l(r (r el el (lr (lr !e l( l( 0n%* 0n%*(n* (n*ee 0 4 S# )n( '(m#l#( *#ene * #ene (l men% !% "#$%5 )e *en+( : "#$%? R&*( (4 071@; 4 8@ 8.- Un( 0($( 0n*#ene 0" '0% !e l)B el0*r#0(%5 *re% !e l% 0)(le% %n !e'e0*)%%. De l( 0($( %e %ele00#n( %ele00#n( (l (B(r )n '0 %e l( &r)e(5 re&#*#n!%e re&#*#n!%e l( &er(0#,n &er(0#,n "(%*( >)e (&(reB0( )n !e'e0*)%. Se( / l( (r#(le (le(*r#( >)e %e !e'#ne 0m el númer !e e6*r(00#ne% ne0e%(r#(% "(%*( >)e (&(reB0( el &r#mer '0 !e'e0*)%5 !e*erm#n(r l( !#%*r#)0#,n !e &r(#l#!(! !e /5 %# l(% e6*r(00#ne% %e "(0en2 (4 S#n re&%#0#,n5 4 0n re&%#0#n( 04 H(ll(r l( ')n0#,n !e !#%*r#)0#,n (0)m)l(!( F364 !e / R&*( (4 V(lre%2 158595:5;55 &r(#l#!(!e%2 81@;5 1;@;5 1@;5 @;5 9@;5 1@;
9 ; b 4 P 3 X = k 4 = 3 43 4k −1 5 7158595....5e*05.. G G %# 6 p 1 5 04F3647 ; k 1 3 4 5 %# ≤ 6 p H15 7158595...5e*0 − G 9.-De*erm#n(r el (lr !e l( 0n%*(n*e 0 &(r( >)e l( ')n0#,n !e'#n#!( &r2
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f 3 x 4 = P 3 X = x 4 =
c x
9
5
6751585.5.5 ..
Se( )n( ')n0#,n !e &r(#l#!(! !e (l+)n( (r#(le (le(*r#( !#%0re*( / 0(l0)l(r l( &r(#l#!(! !e >)e / *me (lre% &(re%. Pr*(2 0 7 8@9
5;
:.- L( &r&r0#,n !e &er%n(% >)e 0n*e%*(n &r 0rre e% )n( (r#(le (le(*r#( 0n*#n)( / 0n ')n0#,n !e !en%#!(! !e &r(#l#!(!
c3 x + 945 %# p 6 p 1 f 3 x 4 = 5 en *r% 0(%% (4 De*erm#n(r el (lr !e l( 0n%*(n*e 0 l( '.!.( F364 4 S# l( &r&r0#,n !e &er%n(% >)e 0n*e%*(n e% (l men% 8;5 0(l0)l(r l( &r(#l#!(! !e >)e *(l &r&r0#,n %e( ( l m=% ;
P 3 X ≤ 5 A; @ X ≥ 5 8;4 R&*(2 (4 8@
4
;.- S)&n+(m% >)e el #n+re% men%)(l en m#le% !e )n#!(!e% mne*(r#(% 3).m4 !e )n#!(!e% '(m#l#(re% !e )n( 0#)!(!5 e% )n( (r#(le (le(*r#( / 0n ')n0#,n !e !en%#!(! !e &r(#l#!(!.
%# ≤ 6 ≤ 1 :kx5 k 3; − x45 %# 1 ≤ 6 ≤ ;
f 3 x 4 =
(4 De*erm#ne el (lr !e l( 0n%*(n*e . 4 C(l0)l(r el &r0en*($e !e )n#!(!e% '(m#l#(re% 0n #n+re% men%)(le% !e ( l m(% 8 m#l ).m. R&*(. (4 7 51
4 ;;
.- Un( e%*(0#,n +(%l#ner( re0#e &r#%#,n %em(n(lmen*e. S# el l)men %em(n(l !e en*(%5 en m#le% !e +(lne%5 e% )n( (r#(le (le(*r#( / 0)( '.!.&. %e (&r6#m( ( l( ')n0#,n 0)( +r('#0( e% l( '#+)r( >)e %#+)e2
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0
1
(4 De*erm#n(r l( '.!.& !e / 4 H(ll(r l( ')n0#,n !e !#%*r#)0#,n (0)m)l(!( !e / *r(B(r %) +r='#0(.
x f 3 x 4 = − x3 x − 84
%# J6J1 %# 1 ≤ 6 p 8 en *r% 0(%%
R&*(. (4 0 7 1 .- El *#em& en "r(% >)e )n( '(m#l#( m#r( *ele#%#,n !)r(n*e el !K( e% )n( (r#(le (le(*r#( / 0n ')n0#,n !e !en%#!(! !e &r(#l#!(!2
%# ≤ 6 p 8 kx 8k %# 8 ≤ 6 p D f 3 x4 = −k 3 x − G4 %# D ≤ 6 p G en *r% 0(%% (4 H(ll(r 0(l0)le l( &r,(#l#!(! !e >)e l( '(m#l#( m#re *ele#%#,n en*re 1 "r(%. 4 De*erm#ne l( ')n0#,n !e !#%*r#)0#,n (0)m)l(!( F364. Gr('#0(r R&*(. (4 7 1@18
5
88@8:
.- S)&n+( >)e el númer !e 0)r%% en >)e e%*= m(*r#0)l(! )n (l)mn e% )n( (r#(le (le(*r#( / 0n ')n0#,n !e &r(#l#!(!2 6 '3647P3/764
1 1@1
8 8@1
9 9@1
: 9@1
(4 De*erm#n(r l( me!#( l( (r#(nB( !e l( (r#(le (le(*r#( /
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; 1@1
4 S# *!% l% 0)r%% %n !e 0)(*r 0r!#*%5 !e*erm#n(r l( ')n0#,n !e &r(#l#!(!5 l( me!#( l( (r#(nB( !el númer !e 0r!#*%. R&*(. (4 951 1585 4 185:
5 85:
.- Un $)e+ 0n%#%*e en e6*r(er (l (B(r *re% '#0"(% ( l( eB !e )n( )rn( >)e 0n*#ene : '#0"(% r$(% (B)le%. Se +(n( %@. 8 &r 0(!( '#0"( r$( %@. 1 &r 0(!( '#0"( (B)l. )e e%*e $)e+ %e( $)%*? R&*(. Se( / l( +(n(n0#( !el $)+(!r. S) !#%*r#)0#,n !e &r(#l#!(! e%2
6 9 : '3647P3/764 ;@9 1;@9 S# C e% l( 0(n*#!(! >)e %e !e&%#*(5 en*n0e%
; @9
1@9
E3/-C47 #m&l#0( C7:8 1.- C(l0)le l( me!#( 0)( !#%*r#)0#,n !e &r(#l#!(! e%2
%# ≤ 6 ≤ 9
8 x @ M5 f 3 x4 = 5
en *r% 0(%%
R&*( me!#( 7 8
11.- El 0%* C !e )n &re0*5 en m#le% !e %le%5 e%*= !(! &r C79/;/ 85 %#en! / el *#em& em&le(!5 )n( (r#(le (le(*r#( >)e er#'#0(
E 3 X − 1 @ 84 8 = 19 @ :5
3 X − 14 8 = 8 E7
(4 De*erm#n(r l( me!#( l( (r#(nB( !e /. 4 C(l0)l(r el 0%* e%&er(! !el &re0*. R&*(. (4 E3/847;5
E3/478 V3/471 4 %@. 91
8 E 3 X − c 4
18 S# e6#%*e5 0(l0)l(r el (lr !e 0 >)e "(0e mKn#m( e%( ')n0#,n !e l( (r#(le (le(*r#( /.
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R&*(. E3/470 19.- H(ll(r V3(/4 1:.-L ')n0#,n !e !en%#!(! !e &r(#l#!(! !e )n( (r#(le / e%*( !(!( &r2
831 − x 4 f 3 x4 =
p 6 p1 &(r( *r% 0(%
Deter m#n ar 2 a4 E3/4
4 V(r3/4
1;.- En )n( '#0#n( "( !% 0m&)*(!r(% A >)e *r(($(n !e m(ner( #n!e&en!#en*e. S# en )n mmen* 0)(l>)#er( l( &r(#l#!(! !e >)e l( m(>)#n( e%*e en m(l e%*(! e% l( &r(#l#!(! !e >)e %l l( m(>)#n( A e%*e en m(l e%*(! e% 9@15 )e %l l( m(>)#n( e%*e en m(l(% 0n!#0#ne%? R&*( 9@8 1.- Sl el !e l( mer0(!erK( >)e re0#e )n 0mer0#(n*e !el '(r#0(n*e A e% !e 0(l#!(! e60e&0#n(l5 m#en*r(% >)e el !e l( mer0(!erK( >)e re0#e el '(r#0(n*e e% !e 0(l#!(! e60e&0#n(l. S#n em(r+ l( 0(&(0#!(! !e '(r#0(0#,n !el '(r#0(n*e e% l#m#*(!(5 5 &r e%*( r(B,n %l el 9 !e l( mer0(!erK( le e% &erm#*#! (!>)#r#r !el '(r#0(n*e 5 el l( (!>)#ere !e A. Se #n%&e00#n( )n em(r>)e >)e (0(( !e lle+(r %e en0)en*r( >)e e% !e 0(l#!(! e60e&0#n(l5 C)(l e% l( &r(#l#!(! !e >)e &ren+( !el '(r#0(n*e A?. R&*(. 5:8@5 1.- L% &r#mer% %n!e% ('#rm(n >)e el &r0en*($e !e ele0*re% >)e *(r#(n &r el 0(n!#*(! D &)e!e %er2 9 0n &r(#l#!(! 5 ; 0n &r(#l#!(! 59 0n &r(#l#!(! 51 (4 S# %e el#+e )n ele0*r (l (B(r )e *e &r D? 4 S# *( &r D )e &er*eneB0( (l 1 !el **(l? 04 R&*(2 51;
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!4 C4 S# %e e%0+en !% le0*re% )e )n !e ell% *e &r D?. e4 R&*( 5: 1.- Un( '(r#0(n*e >)e !#%&ne !e (r#(% m=>)#n(% &(r( &r!)0#r )n $e* *#ene l( me*( !e &r!)0#r !% m#llne% !e ell% en )n (. Se e%*#m( >)e "( )n( &r(#l#!(! !e 59; !e >)e el !e l(% m(>)#n(% (l0(n0en l( me*(5 !e 58; !e >)e el !e l(% m(>)#n(% (l0(n0en l( me*(5 !e 5: !e >)e el !e l(% m(>)#n(% (l0(n0en l( me*(. S# %e %ele00#n( (l (B(r )n( !e l(% m(>)#n(%5 (4 C(l0)l(r l( &r(#l#!(! !e >)e e%*e en*re l(% >)e (l0(nB(rn l( me*( 4 %# e%*( en*re l(% >)e (l0(nB(rn l( me*(5 0(l0)l(r l( &r(#l#!(! !e >)e "(( %#! !el !e l(% m(>)#n(%. R&*(. (4 51 4 588;@517598
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