giup em cam on trc a
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 4
a) Do Cx // AB
⇒ ∠BCx = ∠ABC = 45⁰ (so le trong)
b) Do AB ⊥ AE
DE ⊥ AE
⇒ AB // DE
Mà Cx // AB
⇒ Cx // DE
c) Do Cx // DE
⇒ ∠DCx = ∠CDE = 60⁰ (so le trong)
⇒ ∠BCD = ∠BCx + ∠DCx
= 45⁰ + 60⁰
= 105⁰
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Cách làm ngắn gọn: \(5=\dfrac{5\left(x-1\right)}{x-1}=\dfrac{5x-5}{x-1}=\dfrac{5x+5-10}{x-1}\)
Do đó chọn \(f\left(x\right)=5x+5\) thế vào nhanh chóng tính ra kết quả giới hạn
Còn cách khác phức tạp hơn (có thể sử dụng cho tự luận):
Do \(\lim\limits_{x\rightarrow1}\dfrac{f\left(x\right)-10}{x-1}=5\) hữu hạn nên \(f\left(x\right)-10=0\) có nghiệm \(x=1\)
\(\Rightarrow f\left(1\right)-10=0\Rightarrow f\left(1\right)=10\)
Do đó:
\(\lim\limits_{x\rightarrow1}\dfrac{f\left(x\right)-10}{\left(\sqrt{x}-1\right)\left(\sqrt{4f\left(x\right)+9}+3\right)}=\lim\limits_{x\rightarrow1}\dfrac{\left[f\left(x\right)-10\right]\left(\sqrt{x}+1\right)}{\left(x-1\right)\left(\sqrt{4f\left(x\right)+9}+3\right)}\)
\(=\lim\limits_{x\rightarrow1}\dfrac{f\left(x\right)-10}{x-1}.\dfrac{\sqrt{x}+1}{\sqrt{4f\left(x\right)+9}+3}=5.\dfrac{1+1}{\sqrt{4f\left(1\right)+9}+3}=5.\dfrac{2}{\sqrt{4.10+9}+3}=...\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(x⋮12\)và \(13< x< 75\)
\(\Rightarrow x\in B_{\left(12\right)}\)mà \(13< x< 75\)
\(\Rightarrow x\in\left\{24;36;48;60;72\right\}\)
b) \(6⋮\left(x-1\right)\)
\(\Rightarrow\left(x-1\right)\inƯ_6\)
\(\Rightarrow\left(x-1\right)\in\left\{\pm1;\pm2;\pm3;\pm6\right\}\)
\(\Rightarrow x\in\left\{...\right\}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
c)3(2x-1)-5(x-3)+6(3x-4)=24
<=>6x-3-5x-15+18x-24=24
<=>19x-12=24
<=>19x=36
<=>x=\(\frac{36}{19}\)
d)2x(5-3x)+2x(3x-5)-3(x-7)=3
<=>10x-6x2+6x2-10x-3x-21=3
<=>-3(x-7)=3
<=>21-3x=3
<=>-3x=-18
<=>x=6
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
a)\(R_1//R_2\Rightarrow R_{12}=\dfrac{R_1\cdot R_2}{R_1+R_2}=\dfrac{60\cdot40}{60+40}=24\Omega\)
\(I=\dfrac{U}{R_{tđ}}=\dfrac{12}{24}=0,5A\)
b)\(U_1=U_2=U=12V\)
\(P_1=\dfrac{U_1^2}{R_1}=\dfrac{12^2}{60}=2,4W\)
\(P_2=\dfrac{U_2^2}{R_2}=\dfrac{12^2}{40}=3,6W\)
c)CTM mới: \(R_3nt(R_1//R_2)\)
\(I'=\dfrac{I}{2}=\dfrac{0,5}{2}=0,25A\)
\(R_{tđ}=\dfrac{U}{I'}=\dfrac{12}{0,25}=48\Omega\)
\(R_3=R_{tđ}-R_{12}=48-24=24\Omega\)
a) 2/(2.5) + 2/(5.8) + 2/(8.11) + ... + 2/(98.101)
= 2/3 . (1/2 - 1/5 + 1/5 - 1/8 + 1/8 - 1/11 + ... + 1/98 - 1/101)
= 2/3 . (1/2 - 1/101)
= 2/3 . 99/202
= 33/101
b) 1/(4.7) + 1/(7.10) + 1/(10.13) + ... + 1/(94.97) + 1/(97.100)
= 1/3 . (1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 + ... + 1/94 - 1/97 + 1/97 - 1/100)
= 1/3 . (1/4 - 1/100)
= 1/3 . 6/25
= 2/25