trin 3.
o X6t Phucmg tich cira dii5m e d6i v6i ducmg tron tAm O vd duong trdn 9c6 OE : eA2 :
QD 8F suy ra QE ld titip tuy6n cira ducrngtrdn ?. trdn ?.
YQy FO vd EQ ddu ld ti6p tuyiin cira duong
trdn 3 vd chring ctng ch6n cung FE n€n
^ ^
oFE : QEF .r
Mdi c5c ban tim nhi6u crlch gi6i cira BAI
TOAN 10 NCG sau dAy vd gui ve toa souo
TH&TT tru6c ngdy 20112120t3.
nAl roAx lo NCG" T[nk xl + 7,2 theo
tham so a dtrong, bl€t riing
16- ,2 * ,.,[o --rT = o.
Nguoi ra d6: THAI NHAT pIilJONG
(Cf fucS Nguydn Vdn Tr6i, Cam Nghia,
Cam Ranh, Khdnh Hod)
(7) (10) a PT : PA.PB, Hinh 2 ,r.A (i39,,b W r&o d6. g '1;y/
,'OIAI'IOAN
'EEHrtAYrrilH
(16" bdi to6n giai tich ld mQt dpng to6n di6n
\-rtrintr thucrng g{p trong c6c ki thi giii to6n
tr6n m6y tinh cdm tay cltp Tinh vd c6p Qu6c gia. Nhim girip c6c em hgc sinh chuAn bi 6n
tpp tot vd hudng d6n c6c ki thi, bdi vitit xinduqc gi6i thiqu mQt sO ttti du vd bdi tap ld duqc gi6i thiqu mQt sO ttti du vd bdi tap ld
nhirng dC thi cira c6c So GD-DT trong
-l
nhfrng nim gAn diy. Trong bdi vi6t ndy, ching
t6i dAu ti6n hdnh c6c thao tlc tr€t mhy
tinh VINACAL 5708S PLUS II, CASIO /r -
570W PLUS, hai ddng m6y c6 nhi6u tinh
ndng nh6t dugc B0 GD&DT cho ph6p mang
vdo phdng thi.
r. TINH Gror HAN VA DA,O HAM
CUA HAN{ SO
. oC tinh dao hdm cira hdm s5 tpi di6m xs ta
nhAn H6n ti6p cdc phim @ H t,ic d6 mdn
A: lim
x-+0
Vr.t -\lr;+l
Ldi gidl (VINACAL 570E5 PLUS 11) Ta thlrc
hiQn theo quy hinh b6m phim sau:
@MtCffiffiffiMMffiMlf,mmE@mmmmmmlt mmE@mmmmmmlt
A i r , * i- u-l---MOT t $0 BAI TOAN SIAI TICH MOT t $0 BAI TOAN SIAI TICH
r I t
^ , -J-,,- -a
lflIIil Glllrulil ruililAYIIllH fill TII
TRAN D|NH CU
1*:iI'.,i$fift$iTGy,1ffilpng THpT Gia HQi, Thua Thi6n Hue)
mmffimmmffimE.radusc
k6t qun x * -0,1333333333. EC d6i sO tt pp
phAn v6 han tudn hodn ndy sang ph6n si5 ta 6n
pni- nh, sau II E E I @ @ : E ta
dugck6tquaA- -215'
Ta c6 th6 chuy6n viQc tinh gi6i han tr6n thdnh
tinh dao hdm ctra mOt hdm sO tai m0t di6m
nhd nhfln x6t.
A=timfG)-[(o) = f '(0)
x--+0 x - 0
voi f (x): {6;T -flrx +r
Oe tintr /'(0) ta thlrc hiQn theo quy trinh 6n
phimsau:@H@mmE@mE
mmE@mmffim@mE
MMEEEI
Ta dugc k6t qui A = 4,1333333333. a
hinh hi6n fl,r
S (l)1,=o . Nhap hdm s6 vd *Thi d42. cho hdm s6
nhQp gi6 tri xo , sau d6 An phim EI
. Odi voi m6y tinh VINAC N- 57OES PLUS il
ta c6 th6 tinh gioi h4n cua him s6 tai iliOm
x6 bing c6ch nh6n c6c phim @ m m
hic d6 mdn hinh hi6n thi lim (n)1,-r . Nh0p
hdm sO vd nhap ei fr.r6 , S&u d6 6n phim El.
* Thi dql. T{nh gicti hqn
e,t r
f(r) =-
G;;+h(x+l)
Tinh gia tri gdn dting cila
.!=f,(,).r'[;) .,
[+)+ +, [*)
Lbi gidl pC tintr S ta thUc hiQn theo quy trinh 6n phim sau:
m@mffi {Bitindam} ffi@ffi E
{Bi6n t6ng} mmffiEr@mIIm@E@ H@El@mg@ffitt@E @m@mmmmm@mmEr mmmffi:tm@mriltnmE mffimmmm. ,4\ TORN HQC.....".. <,4d,i> ' cludiua ,.;. Wnaaa$9
Lticd6mdnhinhhi6nthi X=X+l'r ' 1
( tr= \l ' L Xet ham s6 7111 = gt-+t + ln I tr6n (l;+to).
,a, dl "':- ll ,acof,Q)=(3t2+l)ar3*r*1r0.
-L-T-l - drlJr'+2x+ln(x+r).,J1"_r : , -'-'")" 't
\ ' ' tx=T n6n him sO
f (t) d6ng bi6n tr6n (f +oo).
e4ticp mEE. noi An HCn ticp d5u El Doir6pT(3) e f(x)=,f(y) e x- y_
d6n lJri X = 10 thi trCn mdn hinh xu6t hiQn Thay y: x'vdo pT (2),ta duo. c
C : -57.787s8s4. oc t6y ktit qu6 v6i 4 chfr -'*: i " '- r .
so ttrap phin, ta tiiip tr,rc 6n phim @ @ til ?i +5x-1=7"'1t' -1
EJ. 16rquA S = -57,7876. Tt rldy vA sau, a 4x4 -29x3 +21x2 -10x+50 = 0 (*)
nSu kh6ng.c6 gi dlc biEt thi c6c k6t qud d6u Sri dUng chric ndng @ ffi dC giai pT (*) liy 4 chit so thflp phdn.tr
![ng c6ch: ghi vdo mdn hinh pr_(*), sau d6
II. SIIDING TiNTI EOI.{ EITU EE GIAI en H6n ti6p M ffi tt EI ta duo. c pffUCn{CTRiNTIVAIU'pilIONGTR}NH *, =
!,550510257, luu x1 vio 6 nh6 A bing
*Thi dg3. Gidiphuongtrinh 3*:7sinx+r c.a7\ntii5p-phim @ ffi ffi, ec tim nghiQm^ , ^ , '"' '" thft hai ta v6n ghi lai vdo mdn hinh PT(*) r6i ^ , ^ , '"' '" thft hai ta v6n ghi lai vdo mdn hinh PT(*) r6i
ffen \ui+@)' 6n@@EHt" dugc x2 x 6,44g4gg743
Ldi gidlx6themsO 71r; = 3* - 7 sinx - x luunghi6mndyvio 6 nh6 B bing c6ch6n@
Tac6 f'(r)=3'ln3-7cosx-1; ffi H {mdn hinh rairray.@mEffi hiQn sO 8}, dtng ptrim rmgffi Oictr.f "(*) =3* 1n2 3 + 7sinx. chuy6n tltin dAuE,5nffitfrEI 1rnaor,mrr .f "(*) =3* 1n2 3 + 7sinx. chuy6n tltin dAuE,5nffitfrEI 1rnaor,mrr NhQnthAy .f "(x) > 0 vcri Vx e (0;+m) n6n hien s6 t0) tuc n {4I{;8 hay A,B tir
f '(x) conhieunh6tmQtnghiQmthuQc (0;+.o). 4"6 = IU
Do do f (x) c6nhi6u nhdt hai nghiQm thuJc i9'i:: cua phucrng t,j,nh x2 - 8x + 10 = 0' tt
(0;+_)
r'r rrr.,L,4r,B'rsr, Lrruuv
d6 (*) € x - 4f J6. VOy nghiQm cria hQ
phucrngtrinh (x; i= (++J6;4*G),
Dr)ng chric n[ng @ @ A6 gi6i phuong trinh:
g@ m6y vc cnc a9 rad bing c6ch 5n @ @; y) = (+ - Ja;+ - Ja).t
MEI.
^Y
Ghi vdo mdn 3^ - 7 sin(x) - x bdng.,th: rII' cuc rRI ffi s6' prtvr u6N
c6cphimmmffi ffi ffi EImmm,r-"r,...=; --'^',
ffi m E m C. pc ,i-
"shiil; d" @ *ty lvs' 7no
hdm s6
ffi tilGl duqc ,,x0,t474477308, ,i6p; /k):axa +bf +d +dx+e' (a *0)
Anffi &ttEtadu-oc x2 x !,943922627. thod man f(o) =l;fol : -], lzl = -I;
Ktit qui xr = 0,1474; x2 = 1,9439 .a 21 35 139
Il3)= - ^ I I\+)= , )lQ) =-*Thidq4.GidihQphaongtrinh '2'"" 4'"' 2' *Thidq4.GidihQphaongtrinh '2'"" 4'"' 2'
y - \,., gdn&inggidfrdi€ntichcrtatumgidc ABC.
2y' + 5x - 1 : 7tl*3 -t (2) Ldigi,fii(vTNACAL sToESpLUSil).
LdigidlDi6ukiQn x)1, y > O. Tt,f(0) = I *, ra e =].Va"chuongtrinhPT0) 6 PT0) 6 "*3** +lnx - "r3*! +lny (3) gi6ihQ4phuongtrinh4AriUingc6chAnffi Afu ToAN HQC........ @b..... ...................Wis'r16 I -sttudiua w
[il m, nh4p c6c hC sO dC t\m a, b, c, d. Ta tim
duoc hdm so 71x; = i,o -i* * l. "r,ao
s6t hdm s6 ndy ta tim dugc
/ r\ / - 23) ^( - 23)
t{ o: 11, al -fi,-2l,cl J1:-2 l.
\ 4) [ ''-r)tc[{/;-zJ
I
Viy Szac : , AC.a (1., nC) x 32,4105 .a
Lru i.o5i voi m6y vINACAL s70as PLUS il
ta c6 thl5 gi6i duoc hQ 4 phucrng trinh 4 An sO
vd luu tn;c titip dugc c6c nghiQm ndy vdo
c6c bi6n nh6 ffi til l, fil trong m6i trudng EQN.
*Thi clu 6. Iirr cdt'fiAm can tita hdm so
1r = 6,1 l, -r
f--- -
{2.r +V3.r+8
,+Ji
Ldi gidl (VINACAL s70ES PLUS ID.
Do lim_ y = 0 n6n tiQm cfln dung :r = ,-+-J)"
OC tlm ti6m c6n ngang, ta cdn tinh
Dung chric n[ng tinh gi6i hpn cira hdm sO @
m [il, mdn hinh hi6n thr lim ( tr ) I ,-r .
NhQp hdm s6 el-ixl +
x+Ji
cho x c6c gi6 tri rAt l6n nhu 999 999;'
999 999 999; 999 999 999 999 racingduoc
ei6 qn y:Ji hay y =1,4142; cho x c6c
96 fr rat be ntur -999 999; -999 999 999;
-999 999 999 999 ta cung dugc gi6 triy : -Ji hay y x -1,41421. VAy c6 hai tiQm y : -Ji hay y x -1,41421. VAy c6 hai tiQm
c4ndimg lit y = +J2 o t1,4142.a
*Thi dq7" C'ho ham.go
2x2_ 5x+3
" 3x2*-r+1
.Yac din.h totl ct| t{iAnt uin ctia tli thi ham sti
dd t:ho.
t;
Ldi gi,fii. TXE D : IR.. l3x2 -l4x -2 Ta c6 v' (rr' - * +t)2 <(n*' -21x2 - 6x + 3) ..r - . / t- ^ ,) (3*2 -x+l)" \/
Vho chuong ffinh m til A6 giii phucmg trinh
bQcba 13x3 -21x2 -6x+3=O.
[x1 = 1.8005 luuvdo0nhdA
!" :0 e I ,z x 0,2772 luu vdo 6 nh6 B
Lr, = -0,4624 luu vio 6 nhd C.
Sir dlrng chirc n[ng @ tinfr gi6 ta hdm s5
y: f(x) tqic6cgi6q A,B,C (xemD{csanS5 S) ta ttugc h * 0,0539; y2 x 1,8542; S5 S) ta ttugc h * 0,0539; y2 x 1,8542;
!3 * 2,7282.A
rv. GrA rRI LoN r{HAr vA GIA rRI
]\I-tO NHAT CUA HANN SO
*Thi dqr 8. (oi *i HSG MTCT Quing Tri 20t2)
T'im giit tri lan nhat t,it gia tri nhd nhat ,trtt
LE\1-.I
Itit* ,ti .y = I .r* -Yr' I - i/iia . r- -=
"iollI I l_,^l It'L'tl tl(tt.ltl [- r't.(: r,'I _.,] . Liri giai.Edt D: [-16' J, ] , "u t-; , f(x\ = 11 - + f - 3Jfi 12 + * - nWffi .17 Tac6 f'(x) = 4x3 -T*'-21,h7x+1.
Sir dung ffi It dc giai PT / '(x) : 0 tim dusc
xt x 1,4275 (loai); x2 N 0,1824; 4 = -O,9603.Su dung chirc ndng @ tirh duqc Su dung chirc ndng @ tirh duqc
/ (-.6) x 3,057e; f (Jr) x -3,1741;
"f (*z) = -0,9035 ; f (4) x -2,7104.
Suyra -3,1741< f (x) < 3,0579,Yx e D.Dod6 o < lffx)l <3,r74t. Dod6 o < lffx)l <3,r74t.
Vfy max f (x) = 3,1741; min /(;) = 0. trDD DD
},ae aaa. ai 9
zx2 +.,[:x * s
z4\
,.\
v. T'[Ep TUY$]N CUa OO TH.[ HAM SO / '(.6 ) = 27,52t8045 . G6c can tm Uang*T'hi clu 9. (ili thi IflSG 1VTCT' Quic gia Zttt 3) *T'hi clu 9. (ili thi IflSG 1VTCT' Quic gia Zttt 3)
("lu; lti*r^r,j /(r)=e.';*.1';sin4.r+t-nr.,(nin.r*zy. L-t^'(-r'fr6ll'rctqua a = 0,0363 (rad).n
Lrt |'irtlr gii tt'i lrirm.s,i tui , = #,
l,) l)triitt,l tlr,inq.l.- (i.r +h !Lt tir:J, ttr.t.r:rt ,.ttrt I'Tinhc6cgi6i h4nsau