3A

4B

5D

3C

4D

5D

6C

1.

\(y'=\dfrac{3}{\left(x+2\right)^2}\Rightarrow\left\{{}\begin{matrix}y'\left(-1\right)=3\\y\left(-1\right)=-2\end{matrix}\right.\)

Phương trình tiếp tuyến:

\(y=3\left(x+1\right)-2\Leftrightarrow y=3x+1\)

2.

\(y'=2x+3\)

\(\Rightarrow\left\{{}\begin{matrix}y'\left(1\right)=5\\y\left(1\right)=2\end{matrix}\right.\)

Phương trình tiếp tuyến:

\(y=5\left(x-1\right)+2\Leftrightarrow y=5x-3\)

3.

\(y'=\dfrac{-4}{\left(x-1\right)^2}\)

Gọi \(x_0\) là hoành độ tiếp điểm \(\Rightarrow\dfrac{x_0+3}{x_0-1}=2\Rightarrow x_0+3=2x_0-2\)

\(\Rightarrow x_0=5\)

\(\Rightarrow y'\left(5\right)=\dfrac{-4}{\left(5-1\right)^2}=-\dfrac{1}{4}\)

Phương trình tiếp tuyến:

\(y=-\dfrac{1}{4}\left(x-5\right)+2\Leftrightarrow y=-\dfrac{1}{4}x+\dfrac{13}{4}\)

4.

\(y'=2x+2\)

Gọi \(x_0\) là hoành độ tiếp điểm \(\Rightarrow x_0^2+2x_0+4=3\)

\(\Rightarrow x_0^2+2x_0+1=0\Rightarrow x_0=-1\)

\(\Rightarrow y'\left(-1\right)=2.\left(-1\right)+2=0\)

Tiếp tuyến: 

\(y=0\left(x+1\right)+3\Leftrightarrow y=3\)

5.

\(y'=\dfrac{5}{\left(x+1\right)^2}\)

Gọi \(x_0\) là hoành độ tiếp điểm \(\Rightarrow\dfrac{5}{\left(x_0+1\right)^2}=\dfrac{5}{9}\)

\(\Rightarrow\left(x_0+1\right)^2=9\Rightarrow\left[{}\begin{matrix}x_0=2\\x_0=-4\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}y_0=-\dfrac{2}{3}\\y_0=\dfrac{8}{3}\end{matrix}\right.\)

Có 2 tiếp tuyến thỏa mãn:

\(\left[{}\begin{matrix}y=\dfrac{5}{9}\left(x-2\right)-\dfrac{2}{3}\\y=\dfrac{5}{9}\left(x+4\right)+\dfrac{8}{3}\end{matrix}\right.\) \(\Leftrightarrow...\)

6.

\(y'=2x-3\)

Gọi \(x_0\) là hoành độ tiếp điểm \(\Rightarrow2x_0-3=1\Rightarrow x_0=2\)

\(\Rightarrow y_0=2^2-2.3+1=-1\)

Phương trình tiếp tuyến:

\(y=1\left(x-2\right)-1\Leftrightarrow y=x-3\)

6. B
7. D
8. C
9. A
10. A
11. A
12. A
13. A
14. B
15. C
16. B
17. C
18. A
19. C
 

1 T

2 T

3 F

4 T

5 D

6 D

T T F T A D

Em chỉ cần đáp án hay cần giải luôn nhỉ?

Tham khảo nha 

1B 2D 3D 4B 5A 6C 7A 8B 9D 10C 11D 12C 13C 14C 15D 16A 17B 

1 I asked her if she had met my friend

2 He asked me if I could swim

3 Nam told Lan he was writing to her friend that night

4 They told him they gave him a pen

5 Peter told Mary her father had just come to his house

6 Mr Hiep told the pupils he often gave them good advice

7 She told him she had met him at the beach the day before

8 Nam asked Hong if she had been tired the day before

1 She asked Nam where he was going

2 They asked Hoa what her friend had read

9 I asked Peter why he went to her house

10 Lan asked Huong when she would visit her friend?

11 He asked her what her name was

12 Yom asked Mart where she had met his sister

13 Peter asked Daisy if she was writing to his brother

14 Peter told Mary to bring him her pen

15 She told him not to tell her brother about it

16 Mai told Huong to go to her friend's house with her

17 Hong told Nam to try his best

18 He told me not to go out alone at night

19 He asked me if I visited his friend often

20 She asked me if I liked her

21 He asked Hoa what had made her sad

22 Mr Pike asked Mary where she often went

23 She said she would go to visit Nha Trang

24 Mary told Tom she had seen his friend going with her friend

25 I said I would go to visit her

26 Lan told me she gad read my book ten days before

27 Hoa told Hung she had been writing to him

28 She asked him why he hadn't gone to the party the day before

29 Peter asked Daisy where they were going to meet each other the next Sunday

30 he asked Hoa of she had met her friend

1. I asked her if she had met my friend.

2. He asked me if I could him.

3. Nam said to Lan that he was writing to her friend that night.

4. They offered to give him a pen.

5. Peter said to Mary that her father had just come to his house.

6. Mr Hiep said to the pupils that he often gave them good advice.

7. She said to him that she had met him the day before.

8. Nam asked Hong if she had been tired the day before.

1. She asked Nam where he was going.

2. They asked Hoa what her friend had read.

9. They asked Peter why he didn't go to her house.

10. Lan asked Huong when she would visit her friend.

11. He asked her what her name was.

12. Tom asked Mary where she had met his siter.

13. Peter asked Daisy if she was writing to his brother.

14. Peter asked Mary to bring him her pen.

15. She asked him not to tell her mother about it.

16. Mai asked Huong to go to her friend's house with her.

17. Huong encouraged Nam to try his best.

18. He warned her not to go out alone at night.

19. He asked me if I visited his friend often.

20. She asked me if I liked her.

m: \(=x^m\cdot x^2-x^m=x^m\left(x^2-1\right)=x^m\left(x-1\right)\left(x+1\right)\)

n: \(=5\cdot x^m\cdot x^2+10x^2\)

\(=5x^2\left(x^m+2\right)\)

o: \(=5x\left(x-2y\right)+2\left(x-2y\right)^2\)

\(=\left(x-2y\right)\left(5x+2x-4y\right)\)

=(x-2y)(7x-4y)

p: \(=7x\left(y-4\right)^2+\left(y-4\right)^3\)

\(=\left(y-4\right)^2\cdot\left(7x+y-4\right)\)

q: \(\left(4x-8\right)\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)+9\left(8-4x\right)\)

\(=\left(4x-8\right)\left(x^2+6-x-7\right)-9\left(4x-8\right)\)

\(=\left(4x-8\right)\left(x^2-x-10\right)\)

\(=4\left(x-2\right)\left(x^2-x-10\right)\)

m) \(x^{m+2}-x^m\)

\(=x^m\cdot x^2-x^m\)

\(=x^m\left(x^2-1\right)\)

\(=x^m\left(x^2-1^2\right)\)

\(=x^m\left(x-1\right)\left(x+1\right)\)

n) \(5x^{m+2}+10x^2\)

\(=5x^m\cdot x^2+10x^2\)

\(=5x^2\cdot x^m+10x^2\)

\(=5x^2\left(x^m+2\right)\)

o) \(5x\left(x-2y\right)+2\left(2y-x\right)^2\)

\(=5x\left(x-2y\right)+2\left(x-2y\right)^2\)

\(=\left(x-2y\right)\left[5x+2\left(x-2y\right)\right]\)

\(=\left(x-2y\right)\left(5x+2x-4y\right)\)

\(=\left(x-2y\right)\left(7x-4y\right)\)

p) \(7x\left(y-4\right)^2-\left(4-y\right)^3\)

\(=7x\left(4-y\right)^2-\left(4-y\right)^3\)

\(=\left(4-y\right)^2\left[7x-\left(4-y\right)\right]\)

\(=\left(4-y\right)^2\left(7x-4+y\right)\)

q) \(\left(4x-8\right)\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)+9\left(8-4x\right)\)

\(=4\left(x-2\right)\left(x^2+6\right)-4\left(x-2\right)\left(x+7\right)-36\left(x-2\right)\)

\(=4\left(x-2\right)\left[\left(x^2+6\right)-\left(x+7\right)-9\right]\)

\(=4\left(x-2\right)\left(x^2+6-x-7-9\right)\)

\(=4\left(x-2\right)\left(x^2-x-10\right)\)