Cho hàm số  \(f\left(x\right)=x^3-4x\int_0^1\left|f\left(x\right)\right|dx\) và \(f\left(1\right)>0\) . Khi đó \(f\left(4\right)=?\)

Cho hàm số f(x) thỏa mãn \(2xf''\left(x\right)+f\left(x\right)=3x^2\sqrt{x}\)  biết \(f\left(1\right)=\dfrac{1}{2}\) . Tính f(4)

Cho hàm số f(x) thỏa mãn \(\left[f'\left(x\right)\right]^2+f\left(x\right)f''\left(x\right)=15x^4+12x\) ∀x∈R biết

f(0)=f'(0)=1. Tính \(f^2\left(1\right)\)

Cho hàm số y=f(x) liên tục trên R\ {0; -1} thỏa mãn f(1) =-2ln2 và
\(x\left(x+1\right)f'\left(x\right)+f\left(x\right)=x^2+x\) . Tính f(2)

\(sini_{gh}=\dfrac{n_2}{n_1}=\dfrac{1}{1.41}\Rightarrow i_{gh}\approx45^o\)
b. Điều kiện để có phản xạ toàn phần:
 \(\left\{{}\begin{matrix}n_2< n_1\\i\ge i_{gh}\end{matrix}\right.\)(1)
Mà \(i=43^o< 45^0\)
-> Không xảy ra hiện tượng phản xạ toàn phần
 

I. Complete the second sentences so that it means the same as the sentence before:

1. You should water these flowers regularly.

  ->These flowers should  ……………………be watered regularly………………………

2. I last visited London was two years ago.

  -> I haven’t……………………………visited London for two years…………………………………………….……..

3. During dinner, the phone rang.

  ->While I …………………………was having dinner, the phone rang…………………………………

4. What a pity! I don’t have a bike.

  ->I wish…………………………I had a bike………………………………………………….………..

5. “ I am having a workshop on the Environment now”, Peter said.

   -> Peter said that…………………………he was having a workshop on the Environment then …………………………………….…………..

II. Make sentences using the words and phrases:

1.      How about/ give/ presentation/ water/ air/ pollution?

……………………How about giving a presentation about water and air pollution? …………………………………………………………………….

2.      His summer camp/ close/ July 16^th/ last year

………………………………HIs summer camp closed on July 16th last year …………………………………………………………

3. you/ finish/ your homework/ yet ?

          Have you finished your homework yet? ……………………………………………………………………………………….

3.      The foreigner/ said/ he/ not / know/ way/ My Dinh stadium

……………………………The foreigner said that he didn't know the way to My Dinh stadium ……………………………………………………………

4.      Mars/ be / called/ the Red Planet/ because/ its reddish surface.

…………………………………Mars is called the Red Planet because of its reddish surface………………………………………………………

2  The movie theatre which they are building gets two thousand plastic seats 

2/ seats/ they are/ The movie theatre/ building gets/ two thousand/ which/ plastic/./

=> The movie theatre which they are building gets two thousand seats

6/ Mary began using that smart phone three months ago

=> That smart phone has been used by Mary for three months

Cho hàm số y=f(x) xác định trên R và có bảng xét dấu đạo hàm như sau:
 

Biết f(x)>2 ∀xϵR Xét hàm số \(g\left(x\right)=f\left(3-2f\left(x\right)\right)-x^3+3x^2-2020\)   đồng biến, nghịch biến trên các khoảng nào?