II. PHAN BAI TAP
log3(x 2).(log 5X-l) =
Ddp sd X = 3
X = 5.
cau d. Hudng ddn. t - log2 x
Ddp sd. Xi = 4,X2 = 8.
Bai 10. Hudng ddn. Six dung cac phuang phap giai bat phuang trinh mii va Idgarit.
(3Y
cau a. Chia ca tii so va mdu so cho 2" . Dat ^ = I K (^ > 0),
Ddp sd. X < 0 hoac x > 1.
cau b. Hudng ddn. Chu y dilu kien cd nghiem ciia Idgarit.
Ddp sd - V 2 < X < - 1 hoac 1 < x < V2.
cau c. Hudng ddn. Dat t = log x
Ddp sd 0 < X < 10~^ hoac x > 10.
cau d. Hudng ddn. Dat t = log2 x
Ddp sd 0 < X < — hoac x > 2. z
Bai 11. Hutyng ddn. Six dung cac phuang phap tfch phan tiing phdn
cau a. Dat u = Inx, dy =x^dx .
Ddpsd | ( 5 e ^ + l ) .
9
dx
sin X
cau b. Hudng ddn. Dat u=x, dv =
n- - "VS . „
Dapso —-—+ l n 2 .
cau c. Hudng ddn. Dat u= n -x dv = sinxdx
cau d. Hudng ddn. Dat u = 2x + 3 ,dv- e~^dx
Ddpsd 3e - 5.
Bai 12. Hudng ddn. Six dung cac phuang phap ddi bien sd.
- 71 7t
cau a. Hudng ddn. Dat u - cos(— - 4x) ^> du = 4sin(— - 4x)dx. Khi x = 0 o o
1 ^. . n _ V3
thi u = —. Khi X = TT— thi M = - - -
2 24 2
Ddp sd. -5- In 3
o
cau b. Hudng ddn. Dat x = —tan^ ^> dx = ;;—. Khi x = - ^ thi t = —.
5 dcos^^ 5 6
rr. • 3 , , , 71
Khi X = — thi ^ = — -
5 4
cau c. Hudng ddn. Dat u = cosx => du = - s i n x d x . Khi x = 0 thi u = 1. Khi
X = — thi M = 0. z 2 Ddp so . — 35 Cau d. Hudng ddn. Dat u = Vl + t a n x h a y u = 1 + t a n x => 2udu = — cos X
Khi X = - V thi u = 0. Khi X = ^ thi u ^ S .
4 4
n - •' 4V2
Bai 13. Hudng ddn. Six dung cac phuang phap tinh dien tich hinh phdng.
b b
Chii y den cac cdng thiic : S = j | / ( x ) | ( i c , S = ^fix)-gix)\ix va cong thiic can
a a
trung gian de pha bd dau gia tri tuyet ddi va cac tim giao diem ciia hai dd thi. 2 cau a. Hudng ddn. S = (x + l ) d x . - 1 Ddp sd. 6 1 e cau b. Hudng ddn. S = - j In xdx + j l n xdx . Ddpsd 2 ( 1 - - ) . e
Bai 14. Hudng ddn. Six dung cac phuang phap tinh thi tich khd'i trdn xoay.
Giao dilm ciia hai dd thi la nghiem ciia he phuang trinh: y = 2x' y = x^ <=> x = 0 , y = 0 x = 2 , j ' = 8. V = %\ 0 (2x^)^ - ( x ^ ) ^ dx = 'TC\(AX'^ - x ^ l d x = Tt 0^ -')• 4 5 1 7 — x x 2 _ 256Tt 0 35
Bai 15. Hudng ddn. Six dung cac phep toan vl sd phiic. cau a. Hudng ddn. x _ (2 - 5 0 + (4 + li)
3 + 2i r., .- 22 6 . 7 4 cau b. Ddp so X = -— - —i. 5 5 c
9 2
cau d. Huang ddn. Dat t = x ta cd phuang trinh bac hai : ^ - i - 6 = 0 vdi
hai nghiem la ^ = - 2 , ^ = 3.
Ddp sd. X = + Vs , X = ±V2i.
Bai 16. Hudng ddn. Six dung cac tinh chat ciia so phiic, md dun ciia so phiic. cau a. Hudng ddn. \z\<2 o ^Jx + y^ <2 c^ x^ + y^ < 4.
Ddp so.- Tap hgp diem bilu diln sd phiic la phdn trong cua hinh trdn (khdng kl
dudng trdn) cd tam tai gdc toa do, ban kinh 2.
Q u b . | 2 - i | < l o >/x2 + (y - 1)2 < 1 o x^ +iy-l)^ <l.
Ddp sd. Hinh trdn cd tam tai dilm 7(0 ; 1), ban kinh 1.
a u c. Hudng ddn. ^ ( x - 1)^ + iy - 1)^ < i c^ (x - 1)^ + ( j - 1)^ < 1.