[r]
(1)(2)NOi du
oAp Ax vA BIEU DIEM THI THITE C LAN II - KIIOI A -2011
l)Khio sit vi vc a6 tni hirm s5 -2x-3
x-2
1 TXD : R\{z}
2 Su biSn thi6n : + Gini hpn - TiQm cgn
+D6thi:
Gitii phu'o'ng trinh :
lim y =a6p ; hn-l_ ! =-q= d6 thi c6 ti6rn cf.1 dirng litx:2
x+2-
x-+2-li+ y =2 = dd thi c6 tiQm cf.n ngang lity =
+ y' ' = J-< 0 Vx ;e = hdrn sii nghich bi6n tr€n (- -; 2);( 2; +oo)
(*-2)'
v
E? thigiao vdi trpc Oy tai di6m A(0;312);
D6 thi giao v6i fi'uc Ox t4i di6m B (3/2 ;0)
D6 thi nhdn Di6m I Q:2) lA giao cria tiQm c6n lALrn tAm d6i xilng
2) co: M[",?;), xs * 2,y'(xo) =
6+
Phuong frinh ti6p ruyt5n A voi ( C) t4i M: t:y =-:! "(r-ro;+?&:1
l*o -2)- xo - z
To4 dq giao didm A, B cta (A) vd hai tidm cfln n(rje4)t Bea -z;z) \ x\-z )
.Mdt khdc l(?;2) vit AIAB vu6ng t4i I n€n duorg h'dn ngo4i ti6p AIAB duoTrg tr-on cd b6n kinh R:AB/2
Md theo gt, diQn tich ducng trdn bdng 2x > R= Ji o AB =2Ji
| -, (z*-z r'?l , [x^=1
f
<-." - tr' -l?; -,
).] = t -,* - t)' - G+ =, * Ll
=', a M(t: t) vd M (3: 3)
cos2x+ssin(x+
=-z(1) Ekxd:
0,25 0,25 0,2s ,un[,-3n
z\ ( r\
-l.tanln+-l6) l 3/
f sin(x - a J cos(x - a
lsin(x+,r Lcos( r + z
l6)*0 l6)*0 /3)*0 /3)*0 l'* *] l'*
r ktt
-+ -62 r kr +
-2t
( zo.1^ ^ )
e costx +5srnIrc*
2 )=2eZcos'
4,25 0,25 4,25 0,25
r ^ ,, , ; 2r
I cosx=J ltoat) l r=-;+hZ|T
<+l r <+l '
I cosr = I 2n
L 2 L"=- : +kt/,
KOt hgp Ekxd phuo'ng trinh c6 ngiriQm :
(g
lx> e{
t-l^
[x + u Cgc tri : kh6ng c6
+ Bing bi€n thi6n
(tt\(n\
ra c6 : t"[r-AJ ,*["*JJ=-l n6n (t)
x-5cosx-3=0
2r
3
l2x+9> 0
1
,-f 3-V9 +2x +0
(3)^ / .?
2x'13 + JS +zx)-t
-t2 r
\2 (3-Je -2x)
13+Je+zx)- 2x2
bpte l -= <x+21
\3-J9+2x)
2x219 +6^19 a2* +9 +2x\
-T
<x+21
e18 +2x + 6.,1; 2 <2x + 42
Ktit h-op vdi di6u ki6n x6c dinh
x +21
a Jg+z* .4 er<i
2
ta c6 nghipm cta b6t phuong trinh ld : l <.r< lg j
-l1 la2
[,*o t- (
I - lxl,2'
Jl 0\ I
I, = [xe?'dx
0
lx*y=3 lt=3-x
? -
z)
fJ;r' + * rly' *5 = n.' lJx' +: + D[t /(x) =.,6t;+.ft-rt' * s
=
-+)0.='l*r',d*-'l-L*
'14-x') i irl+_*?
Dat u = x,dy =e2t clx - tr=f
Ir
L='[+- oo, ,=t[4-] +at=P, x= 0=>r =z; x=1=>r=v5
o tf4-x'
^14-*/
2
+ r,=
le-f)at=f 4Ji
e2+l 16
+I=-:''*' 3Jj43
lv{A,t = A,C,2 +C,Mt =7zo)t *("Ji)' =9a2;BC2 = AB2 + AC2
-zAB.AC3osl20" =7a2 i BM2 = N +a,f =7d *(rJ t)' =tfr;48 =A4' +zE =(uJs)' +d =zti
Suy ra A,B' = MAr2 + MBz + MB L MAl.
Hinlr ch6p MBAAT vd GABA, c6 chung d6y ld tam gi6c BAA, vd du6ng
cao birrg n€n th6 tich bing
v-t/ v = yMB,t,t, -r/ -l - i -.!a.za.sin:20"=ltJE
= yc'ae,t, = jA4'S^rr =:2atl 5'
2
^ a'JE
=d(A,(A,BM))=#=ffi:m=+
l(r
- A I
\-,f(:*1\s=,,
tt, , X X-3
:.:,=:-:
.J x' +3
./1: - x;'? + s
.f '(x)=6a;"nf4afi =(3-DJx'1 +3 o{"-'=t
l2x" +I\x-27 =0
Phuong trinh thft hai c6 A,=81+54=135=9.15, vd hai nghiQm: ,r=2Y.
hainghi€m ndy ddu bi loai vi nh6 hon vfy, dg.o hiim cria hdm s6 kh6ng rhe d6i
O5 t<icm tra ring cd
(4)VIa r)
VIb
1)
ra f '(3) > 0 n6n .f '(*) > A,Yx2Z
Do d6, gi6 tri nh6 nirdt ciia f (x) khix>2
phuong trinh d6 cho c6 nghi€m (vdi
liL f (2)=^11 +Je .Ctng d6 th6y tyif Q)= co , Tir d6 suy ra: h€ x>2) khi vd chi *>"G *J7
-4a-l -a+I 2 .( 2\
1 = _ €d= = ,[_: , _ j
)
817
_+b
DoBC//(il.'+=+
A( 4a+2i a) suy
eUe+a-1;-a+1) Do AM LBH M tdnunghek,q,c ,a" c(2,!\l3'?
/
\' - /
:x+ y +3 =0 n1n:
Be (d):x+y+3=0 n€n B(b;-b-3)
e b=-4e B(-4;l)
e,Kr1f 4y-lf =17 +1o*y
<> ir - -2y -1* z=(-Zy -1) + yi -(q
1'7 \ =BC I Y-n :1-+b l
\3 '3 )
Gqi I ld trung ditSm AB suy I( ;-1 ;1) Ap dgng hg thric trung ruy6n ftong tam gi6c MAB n6n ta c6 :
MAz +IvB2 =2742 *AB2
2
+ MA2 + W2 nhdnhd e tufr nnl nndi e l,fr L (p)
ndn M ld hinh chi6u ctia i tr€n (p)
Gqi (d) ld duong thing vu6ng g6c v6'i (p) va di qua I suy phuong trinh cria (d) Id :
M ld giao di6m crla (d) va @) n6n ta c6 M(2;1;-1) Ddt z =x+ yi(x,y e R)
li(x + yi)- :l =l(x + yi) - z- rl o l-y - 3 + xil=le - 2) + (y - \rl
x-3 y+1 z -1 -=_=_1aa
l -z:] =r^4=4 (i)
Acgumencio,M)gfLellcz:'-,,"' *" 4 Jz
t l -f- =r-4=-l {3)
l^lt-zy -1)' + y' a 'Jz
Ctng Q)vd (Z)cho ta y - -1, thi tai th1amdncd 1t1vd 1zy
Ydy z =1-i
Goi A(x;y)=B(x;-y) A,B phdn bi|tn€n y* 0 Ae(
Do C (2;0) n€n ACAB cdn rai C
=ACAB ftieCA=AB €(z-x)t + t, =4x2 (2)
lx=-2 >y=0(loqi) Gi;ih€(DvA e)ta itdc: i to ' , iru
L^ - 13 -'Y - 6'76
n,,.n*^e r\ -,\(to tz) lto -tz)
ta co z dtem A,b can rm ta
l,'; n I "" lO; n )
0,25
0,25 0,25 0,25
0,25 0,25 0,25 0,25 0,25 0,25
0,25 4,25
(5)(^
I Y: l-Lf
I
a, :
I I = -3 + 3r = (d, di qua M r(2; -3:0) c6 WCp ur(I; 3; t)
I z =t
ra rttlu : ,41.M/14, =60 +0+ dr;drch/o nhau.Goi MN litfoqn vutng g6cchung cila d,;d, rh1 Mdt ct cobenkinh nh| nh{t trcl rhe void,d, titmit ciu ahig tciin uw
M e d,+ M(4+3r;I-r;-5 -Zt) ; N e dr+ N(Z+ t,;-3 +3t,;r)
I tutY .^ =O l-tqr -2t'=lZ lr = -I
\m.r,=o o \ ,r* rtt'=9o {r'=t +M(r;2;-3);N(3;0;1)
M{t ctu &to-ng ki;h MN cJ ftn r (2;1; -t1 c J u ah nin n = J e
P hndng rriih mdt c d7t t d : (x - 2)' + (y- 1)t + (z + I)2 = 6
TiQm cAn xi€n (A): y = x + m2
t,m
y =1 ;>0,Vx+1:>
(x -r)'
a
Y4y m:_Z
0,25
TU M(1; 5) e (A):+ m = 12.
*2 -2* +1-m
{t -1)2
<+A'<0 em<O