20142smatleccion417h00solucion
TRANSCRIPT
-
7/25/2019 20142SMatLeccion417H00SOLUCION
1/4
!"#$%'% )%& *+$#,-.&/ 01+/2# 3 '. 4
"#$%"&' #%(")*+) (+&*,-$.*$' /"& &*,+)'&0'$%&,'/ /" $*".$*'# .',%)'&"# 1 2',"23,*$'#
/"('),'2".,+ /" 2',"23,*$'#$%)#+ /" .*4"&'$*5. 6789 :6#;
&"$$*5. 9 < :8=>77;?%'1'@%*&A /*$*"2B)" 7C /" 6789
# + & % $ * 5 . D ) E B ) * $ '
,"2' 8 :6F GHIJKL; /MJMNOPIMA QM LMN GKLPRSMA MS JTNOPIK PIQMGMIQPMIJM QM SU VUNPURSM x MI MSQMLUNNKSSK QMS RPIKOPKW
x
y23
! y3
x3
"
#
$$
%
&
''
16
#KSHXPYIW
5%6 '#7%6 .6).8/9/8#'%6 .2 ." $/2%:/% '. ;.&:/2% 2% '.$. 8%27.2.& # "# ?#&/#$". x@ ,-. .6 6.:.A#27. # '.8/& ,-. x6. .28-.27 .".?#'%
#" .B)%2.27. 8.&%C D." 7>&:/2% +.2." 6%"#:.27. 6. 8%26/'. x)# )"#27.#& "# .8-#8/E2=
x
1
2
!
"##
$
%&&
16'i
x'3
2
!
"##
$
%&&
i
=x0
! x
1
216!i( )!
3
2i
= x0
F. /+-#"#2 "%6 .B)%2.27.6=1
2
16! i
( )!
3
2
i = 0 !3
8 0
2 2
ii! ! =
! 8! 2i = 0 ! i = 4
!27%28.6@ ." 7>&:/2% ,-. 2% 8%27/.2. "# ?#&/#$". x .2 ." '.6#&&%""% '." $/2%:/% .6 ." ,-/27%C
G-/27% 7>&:/2%=16
4
!
"##
$
%&&
x
y23
!
"
##
$
%
&&
16'4
' y3
x3
!
"##
$
%&&
4
=
16!
4!12!
x6
y8
!
"#
$
%& y
4 3
x6
!
"#
$
%&
=
16( ) 15( ) 14( ) 13( ) 12!( )4( ) 3( ) 2( ) 1( ) 0!( ) 12!( )
1
y20 3
!
"#
$
%&=
1820
y20 3
-
7/25/2019 20142SMatLeccion417H00SOLUCION
2/4
!"#$%'% )%& *+$#,-.&/ 01+/2# H '. 4
)ZRNPXUW
*QMIJP[PXU XKNNMXJUOMIJM SKL XKOGKIMIJML QMS JTNOPIK \MIMNUS MI MS QMLUNNKSSK QMS RPIKOPKQM .M]JKI^)MLHMSVM XKNNMXJUOMIJM SU MXHUXPYI GUNU MS M_GKIMIJM QMS JTNOPIK PIQMGMIQPMIJM^%JPSP`U MS VUSKN MIXKIJNUQK GNMVPUOMIJM D QMJMNOPIU MS JTNOPIK aHM LM RHLXU^
F GHIJKL
87 GHIJKL87 GHIJKL
,"2' 6 :6F GHIJKL; %IU IHMVU JMKNbU XPMIJb[PXU GNKGKIM aHM SU OMcKN OUIMNU QM JNURUcUN SU JPMNNUGUNU LMORNUN [NMcKSML XKILPLJM MI LMORNUNSKL MI GUaHMJML QM 87 LMOPSSUL XUQU HIKA QM SU LP\HPMIJMOUIMNUW MS GNPOMN QbU LPMORNU 6 GUaHMJMLA MS LM\HIQK CA MS JMNXMNK 9A MS XHUNJK 8dA MS aHPIJK CA MSLM_JK e6A MS LTGJPOK 8dA MS KXJUVK d9 D ULb LHXMLPVUOMIJM fULJU JMNOPIUN JKQU SU GNKVPLPYI QMLMOPSSUL QM [NMcKSML^ #P HI U\NPXHSJKN XHMIJU XKI 86A=77 LMOPSSUL QM [NMcKSML D QMXPQM LMORNUNSULOMQPUIJM MLJU IHMVU JMKNbU XPMIJb[PXUA gMI XHhIJKL QbUL MS U\NPXHSJKN JMNOPIUNh QM LMORNUN JKQUL SULLMOPSSULi
#KSHXPYIW
5.I.2'% '.7.2/'#:.27.@ 6. %$6.&?# ,-. .B/67.2 '%6 8%:)%&7#:/.27%6 '/9.&.27.6 '. )&%+&.6/%2.6+.%:>7&/8#6=
1 2 4 8 ...S = + + +
2 8 16 32 ...S = + + +
F. /2'/8# ,-. "%6 )#,-.7.6 7/.2.2 3J 6.:/""#6@ .27%28.6 6. 7/.2.2=12,700
10=1,270
)#,-.7.6C
F.+K2 "# 8%2'/8/E2 '#'#=
S1+ S
2=1270
F. &..:)"#L#2 )%& "# .B)&.6/E2 '. "# 6-:# '. n 7>&:/2%6 '. -2# )&%+&.6/E2 +.%:>7&/8#@ "-.+%
&.6-."?. "# .8-#8/E2=
2 1! 2n( )
1! 2+
8 1! 2n( )
1! 2=1,270 ! 2 2
n
!1( )+8 2n !1( ) =1,270
! 2 2n( )! 2+8 2n( )!8 =1,270 ! 10 2n( ) =1,280 ! 2 128n =
! 7n =
M#'# -2# '. "#6 H )&%+&.6/%2.6 7.2'&1 N 7>&:/2%6@ .6 '.8/&@ 34 7>&:/2%6 .2 7%7#"C
0%& "% 7#27%@ ." #+&/8-"7%& '.:%&1 34 'O#6 )# 6.:$& 7%'#6 "#6 6.:/""#6C
)ZRNPXUW
(SUIJMU NMSUXPKIML OUJMOhJPXUL U JNUVTL QM MXHUXPKIML HJPSP`UIQK SUL XKIQPXPKIML QMSGNKRSMOU^)MLHMSVM XKNNMXJUOMIJM SU MXHUXPYI aHM GSUIJMY D QMJMNOPIU MS VUSKN QM SU VUNPURSM^$USXHSU MS VUSKN QM SU LHOU LKSPXPJUQU^
87 GHIJKL
87 GHIJKLF GHIJKL
-
7/25/2019 20142SMatLeccion417H00SOLUCION
3/4
!"#$%'% )%& *+$#,-.&/ 01+/2# P '. 4
,"2' e :6F GHIJKL; $KILPQMNM SU [HIXPYI f :X!YQM[PIPQU GKN f x( ) =x2 ! 2x +1
2x2 !x !1^
U; g$HhS ML MS XKIcHIJK X QM OUDKN XUNQPIUSPQUQ GKLPRSM GUNU aHM f LMU HIU [HIXPYIi
R; "I XULK QM M_PLJPNA QMJMNOPIM SUL ULbIJKJUL VMNJPXUSML H fKNP`KIJUSML^ BKLaHMcM SU \Nh[PXU QM f ^
X; /MJMNOPIM MS XKIcHIJK Y GUNU aHM f LMU HIU [HIXPYI LKRNMDMXJPVU^
#KSHXPYIW
5# &.+"# '. 8%&&.6)%2'.28/# .6=
y =
x !1( )2
x !1( ) 2x+1( )=
x !1
2x +1
!27%28.6@ 6-6 &.67&/88/%2.6 6%2=
x!1" 0
x "1
#
2x+1" 0
x " ! 12
;% 6. 8%26/'. ." ?#"%& x Q 3@ )%&,-. +.2. -2# /2'.7.&:/2#8/E2 :#7.:17/8# .2 "# &.+"# '.
8%&&.6)%2'.28/#C
! dom f =X =! " "1
2,1
#$%
&'(
5# #6O2'%7# ?.&7/8#" .6= x = !1
2
5# +&19/8# '. "# 9-28/E2 .6=
!27%28.6@ rg f =! ! 0,1
2
"#
$
%&
'
x
y
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
-4
-3
-2
-1
0
1
2
3
4
-
7/25/2019 20142SMatLeccion417H00SOLUCION
4/4
!"#$%'% )%& *+$#,-.&/ 01+/2# 4 '. 4
0# "# #6O27%7# R%&/L%27#"@ 6. 7/.2.=
y =x
2!2x+1
2x2! x!1
=
x2!2x+1
x2
2x2! x!1
x2
=
x2
x2!
2x
x2 +
1
x2
2x2
x2 !
x
x2!
1
x2
=
1!2
x+
1
x2
2!1
x+
1
x2
F. ?.&/9/8# ,-.@ 8-#2'% x!" @ "# 9-28/E21
2y! @ .67% .6@ 8%2 #6O2'%7# R%&/L%27#" .2 y =
1
2
0# ,-. f6.# 6%$&.I.87/?#@ Y =!! 0,
1
2
"#$
%&'
)ZRNPXUW
U; "LGMXP[PXU XKNNMXJUOMIJM MS QKOPIPK QM SU [HIXPYI^ F GHIJKL
R; /MJMNOPIU SUL ULbIJKJUL D RKLaHMcU XKNNMXJUOMIJM SU \Nh[PXU QM SU [HIXPYI^ 87 GHIJKL
X; "LGMXP[PXU XKNNMXJUOMIJM MS XKIcHIJK 1^ 87 GHIJKL
,"2' 9 :6F GHIJKL; /UQU SU \Nh[PXU QM SU [HIXPYI f :X!YW
U; /MJMNOPIM MS VUSKN QM VMNQUQ QMW !x"dom f f #x
( )= f x
( )
$
%
&
'
R; $USXHSM MS VUSKN IHOTNPXK QMWf !1( )+ 2f 0( )! f 2( )
4f 3( )! f 4( )
#KSHXPYIW
#S 5# '.9/2/8/E2 '#'# 8%&&.6)%2'. # "# '. -2# 9-28/E2 )#&@ ).&% +&19/8#:.27. 6. %$6.&?# ,-. "#
9-28/E2 2% 7/.2. 6/:.7&O# 8%2 ." .A. YC T2 )%6/$". 8%27.A.:)"% 6. 7/.2. 8%2 ! !! !! ! !)-.6
! !! ! ! ! !!5# )&%)%6/8/E2 .6 UV5FVC
$S
5%6 ?#"%&.6 )#&8/#".6 6%2=
f !1( ) = 0 f 0( ) =1 f 2( ) = !1 f 3( ) = !2 f 4( ) = !1
!27%28.6@f !1( )+ 2f 0( )! f 2( )
4f 3( )! f 4( ) =
0+ 2(1)! (!1)
4(!2)! (!1)=
2+1
!8+1= !
3
7
)ZRNPXUW
U; /MQHXM MS JPGK QM QM[PIPXPYI US XHUS LM fUXM NM[MNMIXPU D XKIXSHDM aHM SU GNKGKLPXPYIML [USLU^
87 GHIJKL
R;
"VUSZU XKNNMXJUOMIJM XUQU VUSKN D KRJPMIM MS NMLHSJUQK^ 8F GHIJKL
x
y
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
-4
-3
-2
-1
0
1
2