Toán full 2019 ver 2

HDedu - Page 10

HDedu - Page 14

x(x y 1) 3 0 (1)

(x,y )

5(x y) 1 0 (2)

3(2; )

x – 2y – 1 = 0 (do x + y 0 x 1 và y 0)

x = 2y + 1

(2y 1) 2y y 2y 2(y 1)2y(y 1) 2(y 1) 2y 2 (do y + 1> 0 y 0)

4

x y 1(*)

1 1,

4 4

HDedu - Page 55

5x y 4xy 3y 2(x y) 0xy(x y ) 2 (x y)

= HD

y2 – (4x + 8)y – 5x2 + 16x + 16 = 0

2 y 5x 4' 9x

5

2 2

12x 2xy y

2

y xy 5x 2

HDedu - Page 57

u v

4

(3)(4)

x y

23xy2

12

32

HDedu - Page 58

x 1 y(y x) 4y (1)(x 1)(y x 2) y (2)

x 1 y x 2 1y

7

x y xy 3

x 1 y 1 4

HDedu - Page 59

HDedu - Page 60

,

1; 1

2 2

1;1 2

6 (a) (3 ; 1), 1 ;13 . (b) 3 13 ;0 ,

2

3 13; 4 2

HDedu - Page 61

Hình học 11

HDedu - Page 85

HDedu - Page 100

Lượng giác 11

HDedu - Page 115

HDedu - Page 133

HD's

HDedu - Page 134

Hình học 12

HDedu - Page 162

un + 1 = unq (n *)

n 1 n

uqu

u

2

2, n *)hay uk – 1 + uk + 1 = 2uk

2

k k 1 k 1

u u uhay |u |k u uk 1 k 1 (k 2)

(n *)

n

n(u u )S

n[2u (n 1)d]

S

2

1 5

1 1

1

14u

d5

u (1 q )S

www.tuhoc.edu.vn

htttp://tuhoc.edu.vn/blog

(a) d = 2012(b) d = a

13

2(1 64 2)S

2 1

1

1q2

u 2

thì S20 1023 2

512( 2 1)

HDedu - Page 189

f'(x) < 0 f(x) = 0

HDedu - Page 190

12

HDedu - Page 191

x x

x

11

dx ln | x | Cx

1 dx tan x Ccos x

1 dx cot x Csin x

HDedu - Page 308

I ln|u| C ln|x +x +5| Cu

= HD

HDedu - Page 309

I 2cos 2x dx I 2x sin x dx

HDedu - Page 310

2 1

Q(x) a x x x mx n

HDedu - Page 311

(x 1)(x 2) x 1 x 2

x 3x 2

A(x 2) B(x 1) (A B)x (2A B)(x 1)(x 2) (x 1)(x 2)

x 2x 1ln x 5ln|x - 2| C

HDedu - Page 313

www.tuhoc.edu.vn

htttp://tuhoc.edu.vn/blog

2x 5 1

x

I 2x 8ln x 2 C2

1 cos 2x cos x

2

3

3

3sin x sin3x sin x

43cos x cos3x cos x

cos3x cos 3x cos 3x C.

HDedu - Page 318

21cosa cosb [ cos(a b) cos(a b)]

21sina sinb [ cos(a b) cos(a b)]

1 dx cot x Csin x

2

2

1 dx 1tan(ax b) C

acos (ax b)

dx cot(ax b) C

asin (ax b)

VD7: Tính các nguyên hàm:

= HD(a)

Ta có: T2 = 2

2

1(1 tan x)dx dx tan x C

cos xVD8: Tính các nguyên hàm:

= HD

Ta có:

2 1

2 9

3 10

4 11

4 12

T cos 2x(sin x cos x)dx

4 3

3 4

T tan 2x tan 2x x+C

3 12

T cot (3x 1) cot(3x 1) x+C

HDedu - Page 323