Chỉ em câu 3 với ạ
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`3)(x+4)/(x-3)-(x-3)/(x+4)=(x^2+18x+7)/(x^2+x-12)`
`đk:x ne 3,x ne -4`
Nhân 2 vế với `(x-3)(x+4) ne 0` ta có:
`(x+4)^2-(x-3)^2=x^2+18x+7`
`<=>x^2+8x+16-x^2+6x-9=x^2+18x+7`
`<=>14x+7=x^2+18x+7`
`<=>x^2+4x=0`
`<=>x(x+4)=0`
Vì `x ne -4=>x+4 ne 0`
`<=>x=0`
Vậy `S={0}`
\(\frac{1}{12}-\left(-\frac{1}{6}-\frac{1}{4}\right)\)
\(=\frac{1}{12}-\left(-\frac{2}{12}-\frac{3}{12}\right)\)
\(=\frac{1}{12}+\frac{2}{12}+\frac{3}{12}\)
\(=\frac{1}{2}\)
Thanks bạn cute Jeon Koo Koo nhìu nha , tớ cảm ơn pạn rất nhìu :3
4a.
\(y'=\dfrac{1}{cos^2x}+cosx-2=\dfrac{cos^3x-2cos^2x+1}{cos^2x}=\dfrac{\left(1-cosx\right)\left(1+cosx\left(1-cosx\right)\right)}{cos^2x}>0\) ; \(\forall x\in\left(0;\dfrac{\pi}{2}\right)\)
\(\Rightarrow\) Hàm đồng biến trên \(\left(0;\dfrac{\pi}{2}\right)\)
4b.
\(y'=-sinx-1\le0\) ; \(\forall x\in\left(0;2\pi\right)\)
\(\Rightarrow\) Hàm nghịch biến trên \(\left(0;2\pi\right)\)
c.
\(y'=-sinx-\dfrac{1}{sin^2x}+2=\dfrac{-sin^3x+2sin^2x-1}{sin^2x}=\dfrac{\left(sinx-1\right)\left(1-sin^2x+sinx\right)}{sin^2x}\)
\(=\dfrac{\left(sinx-1\right)\left(cos^2x+sinx\right)}{sin^2x}< 0\) ; \(\forall x\in\left(0;\dfrac{\pi}{2}\right)\)
\(\Rightarrow\) Hàm nghịch biến trên \(\left(0;\dfrac{\pi}{2}\right)\)
4d.
\(y=cosx+sinx.cosx=cosx+\dfrac{1}{2}sin2x\)
\(y'=-sinx+cos2x=-sinx+1-2sin^2x\)
\(y'=0\Leftrightarrow\left[{}\begin{matrix}sinx=-1\\sinx=\dfrac{1}{2}\end{matrix}\right.\)
\(\Rightarrow x=\left\{\dfrac{\pi}{6};\dfrac{5\pi}{6};\dfrac{3\pi}{2}\right\}\)
Bảng biến thiên
Từ BBt ta thấy hàm đồng biến trên các khoảng \(\left(0;\dfrac{\pi}{6}\right)\) và \(\left(\dfrac{5\pi}{6};2\pi\right)\)
Hàm nghịch biến trên \(\left(\dfrac{\pi}{6};\dfrac{5\pi}{6}\right)\)
5 since we last met our uncle
6 were pen pals 2 years ago
started being pen pals 2 years ago
7 not gone to London for 2 years
2 years since we last went to London
we went to London was 2 years ago
8 have never visited HN before
9 2 weeks since she last phoned home
10 seen his brother for nearly 20 years
11 seen our grandfather for 2 years
12 we went to the concert was a year ago
13 Linda talked to me was many years ago
14 we went to the beach was 10 years ago
15 taught English at this school since January 10th
16 I took photographs was 2 years ago
17 6 months since John last had his hair cut
18 we have seen this man here
19 never been to England before
20 the first time I have read a romantic story
21 she wrote to me was in March
22 taught the children in that remote village for 2 years
23 been married for 7 years
24 not written to me for years
1)
Tóm tắt :
R1 = 5Ω
R2 = 5Ω
UAB = 12V
a) Rtđ = ?
b) I = ?
Điện trở tương đương
\(R_{tđ}=R_1+R_2\)
= 5 + 5
= 10 (Ω)
b) Cường độ dòng điện chạy qua đoạn mạch
\(I=\dfrac{U}{R_{tđ}}=\dfrac{12}{10}=1,2\left(A\right)\)
Chúc bạn học tốt