I i;+ * vh x,*r xn)O n6n (x,) ld d6Y
KhiI <a<a th'i limx :4 I
Suy ra (x,) ld ddy c6 gidi han ld 1.
o =1 ,ahi d6 (x,) th ddy hang
l*,=o
{
l*,,, = 3x3 -1x]+5x,'
C6 rdt nhi6u bangrli ldi gi6i (r€n 50 bdi) <ldu giii dring theo c6ch da tdnh bdy 6 tren.
NGUYEN VAN MAU
*Bni TI2l398. Cho trr tli1n ABCD. Tint rdp
hgp tliem P ndm trong tri' tli€n sao cho
xd,+ yd p+zcl1 +td,r =c, vdi.r, .\', :, t. c ld cdc
hcing s6' dttong t'ho trtrJc t'ti cl ,.clB.d1',dD
lin ltrtt !t) t'ric khttiirtll t'iit:h ttl P diit t'tit' tttdt BCD, CDA, DAB, ABC nrctttg tirtg t'tict tLi'di[)n. Ldi gitii. Ta cdn c6 m6t bd dc.
Bd dA. Cho didm O, vectd i vd sd fr. Tap h-o-p
c6c didmP sao cho OF.; =k hm6t m4t phang.
Chmg minh bd d€.
Ldy didm Po sao cnc Odtti ua OFo.i:t
(d6 dhng kidm tra r[ng Po tdn tai vd duy nhdt). Goi (a) ld mat phing di qua Po vi ru6ng g6c
vclt u. latnav
OP.u:keOP.u=OPo.u
* (oP -oh) i = o o P;P.;= Q s P e (.a).
Tr& lai giii Bdi todnTl2.
Goi 1 th tam mat cdu n6i tidp cria trl diOn
ABCD. Gqi X Y, Z,T theo thrl tu ld hlnh chidu
cia I tr€n c6c mat phang (BCD), (CDA),(DAB), (ABC). (DAB), (ABC).
V6i m6i didm P nam trong trldi6n, gor Po, Pu,
Pr, Po theo thrl tu li hinh chidu cira P trOn
mat phing (BCD), (CDA), (DAB), (ABC). Goi (a) mit phing gdm ciic didm P thoi m6n didu kiOn
rt (, tx + y tv + rTZ * tr)=r(t -(x + y + z +t)r)(xem Bd dd tron). (xem Bd dd tron).
Gqi (1, ld giao cia (a) vh midn trong cfia tt1
d\€n ABCD.
Chri i ring cdc vecto7rt,ft,7z,7 theo thrltq cing hucrng va cdc vectofl,4,F4d, tq cing hucrng va cdc vectofl,4,F4d,
theo dinh li hlnh chi6u, tathdy K€i ludn. Ddy (x,) co
t rl
vd chi khi a e | 0:: l.
| 2)
gi6i han hfru han kht
Khi a=0 th) limx, =Q.Khi 0<a<1 thi limx,:1. Khi 0<a<1 thi limx,:1.
.a 11
Khi I <a<a th'i limx. :4. I22 22
FNnan x6t. Bii nly ld su tuong tu nhu dd thi hoc sinh
gi6i Qu6c gia ndm 2005 ddi vdi d6y sd (x,) duoc cho nhu sau
TONN HQC