Para 1 - b

Para 2 - a

Para 3 - c

T - F - T - T - NG

1 B

2 A

3 D

4 D

5 A

2.B (t/c của giới hạn)

6.B H/s ko x/đ với x = 0 -> Ko liên tục tại đ x = 0 

17.C

24. \(\lim\limits_{x\rightarrow\left(-1\right)^-}\dfrac{2x+1}{x+1}\)  . Thấy : \(\lim\limits_{x\rightarrow\left(-1\right)^-}2x+1=2.\left(-1\right)+1=-1\)

\(\lim\limits_{x\rightarrow\left(-1\right)^-}x+1=0\)  ; \(x\rightarrow\left(-1\right)^-\Rightarrow x+1< 0\).

Do đó : \(\lim\limits_{x\rightarrow\left(-1\right)^-}=+\infty\)  . Chọn B 

33 . B 

Trên (SAB) ; Lấy H là TĐ của AB ; ta có : SH \(\perp AB\)  ( \(\Delta SAB\) đều ) ; HC \(\perp AB\) ( \(\Delta ABC\) đều ) 

Ta có : (SAB) \(\perp\left(ABC\right)\)  ; \(\left(SAB\right)\cap\left(ABC\right)=AB;SH\perp AB\)

\(\Rightarrow SH\perp\left(ABC\right)\)

\(SC\cap\left(ABC\right)=C\) . Suy ra : \(\left(SC;\left(ABC\right)\right)=\widehat{SCH}\)

Có : \(SH\perp HC\) => \(\Delta SHC\) vuông tại H 

G/s \(\Delta\)ABC đều có cạnh là a \(\Rightarrow AB=a\)

\(\Delta SAB\) đều => SA = SB = AB = a 

Tính được : \(SH=HC=\dfrac{\sqrt{3}}{2}a\)

\(\Delta SHC\) vuông tại H : \(tan\widehat{SCH}=\dfrac{SH}{HC}=1\)

\(\Rightarrow\widehat{SCH}=45^o\) => ... 

4.

\(\lim\limits_{x\rightarrow8}f\left(x\right)=\lim\limits_{x\rightarrow8}\dfrac{\sqrt[3]{x}-2}{x-8}=\lim\limits_{x\rightarrow8}\dfrac{x-8}{\left(x-8\right)\left(\sqrt[3]{x^2}+2\sqrt[3]{x}+4\right)}=\lim\limits_{x\rightarrow8}\dfrac{1}{\sqrt[3]{x^2}+2\sqrt[3]{x}+4}\)

\(=\dfrac{1}{4+4+4}=\dfrac{1}{12}\)

\(f\left(8\right)=3.8-20=4\)

\(\Rightarrow\lim\limits_{x\rightarrow8}f\left(x\right)\ne f\left(8\right)\)

\(\Rightarrow\) Hàm gián đoạn tại \(x=8\)

5.

\(\lim\limits_{x\rightarrow0^+}f\left(x\right)=\lim\limits_{x\rightarrow0^+}\dfrac{\sqrt[]{1+2x}-1+1-\sqrt[3]{1+3x}}{x}=\lim\limits_{x\rightarrow0^+}\dfrac{\dfrac{2x}{\sqrt[]{1+2x}+1}-\dfrac{3x}{1+\sqrt[3]{1+3x}+\sqrt[3]{\left(1+3x\right)^2}}}{x}\)

\(=\lim\limits_{x\rightarrow0^+}\left(\dfrac{2}{\sqrt[]{1+2x}+1}-\dfrac{3}{1+\sqrt[3]{1+3x}+\sqrt[3]{\left(1+3x\right)^2}}\right)=\dfrac{2}{1+1}-\dfrac{3}{1+1+1}=0\)

\(f\left(0\right)=\lim\limits_{x\rightarrow0^-}f\left(x\right)=\lim\limits_{x\rightarrow0^-}\left(3x^2-2x\right)=0\)

\(\Rightarrow\lim\limits_{x\rightarrow0^+}f\left(x\right)=\lim\limits_{x\rightarrow0^-}f\left(x\right)=f\left(0\right)\)

\(\Rightarrow\) Hàm liên tục tại \(x=0\)

6.

\(\lim\limits_{x\rightarrow0^+}f\left(x\right)=\lim\limits_{x\rightarrow0^+}\dfrac{\sqrt[]{4x+1}-\sqrt[3]{6x+1}}{x^2}\)

\(=\lim\limits_{x\rightarrow0^+}\dfrac{\sqrt[]{4x+1}-\left(2x+1\right)+\left(2x+1-\sqrt[3]{6x+1}\right)}{x^2}\)

\(=\lim\limits_{x\rightarrow0^+}\dfrac{\dfrac{-x^2}{\sqrt[]{4x+1}+2x+1}+\dfrac{x^2\left(8x+12\right)}{\left(2x+1\right)^2+\left(2x+1\right)\sqrt[3]{6x+1}+\sqrt[3]{\left(6x+1\right)^2}}}{x^2}\)

\(=\lim\limits_{x\rightarrow0^+}\left(\dfrac{-1}{\sqrt[]{4x+1}+2x+1}+\dfrac{8x+12}{\left(2x+1\right)^2+\left(2x+1\right)\sqrt[3]{6x+1}+\sqrt[3]{\left(6x+1\right)^2}}\right)\)

\(=\dfrac{-1}{1+1}+\dfrac{12}{1+1+1}=\dfrac{7}{2}\)

\(f\left(0\right)=\lim\limits_{x\rightarrow0^-}f\left(x\right)=\lim\limits_{x\rightarrow0^-}\left(2-3x\right)=2\)

\(\Rightarrow\lim\limits_{x\rightarrow0^+}f\left(x\right)\ne\lim\limits_{x\rightarrow0^-}f\left(x\right)\)

\(\Rightarrow\) Hàm gián đoạn tại \(x=0\)

7.

\(\lim\limits_{x\rightarrow0^+}f\left(x\right)=\lim\limits_{x\rightarrow0^+}\dfrac{\sqrt[]{1+2x}-\left(x+1\right)+\left(x+1-\sqrt[3]{1+3x}\right)}{x^2}\)

\(=\lim\limits_{x\rightarrow0^+}\dfrac{\dfrac{-x^2}{\sqrt[]{1+2x}+x+1}+\dfrac{x^2\left(x+3\right)}{\left(x+1\right)^2+\left(x+1\right)\sqrt[3]{1+3x}+\sqrt[3]{\left(1+3x\right)^2}}}{x^2}\)

\(=\lim\limits_{x\rightarrow0^+}\left(\dfrac{-1}{\sqrt[]{1+2x}+x+1}+\dfrac{x+3}{\left(x+1\right)^2+\left(x+1\right)\sqrt[3]{1+3x}+\sqrt[3]{\left(1+3x\right)^2}}\right)\)

\(=\dfrac{-1}{1+1}+\dfrac{3}{1+1+1}=1\)

\(f\left(0\right)=\lim\limits_{x\rightarrow0^-}f\left(x\right)=\lim\limits_{x\rightarrow0^-}\left(2x+3\right)=3\)

\(\Rightarrow\lim\limits_{x\rightarrow0^+}f\left(x\right)\ne\lim\limits_{x\rightarrow0^-}f\left(x\right)\)

\(\Rightarrow\) Hàm gián đoạn tại \(x=0\)

a) CuO + 2HCl → CuCl2 + H2O                    (1)

     ZnO + 2HCl → ZnCl2 + H2O                    (2)

b) Gọi số mol CuO, ZnO lần lượt là x, y

mhh = mCuO + mZnO → 80x + 81y = 12,1                              (*)

nHCl = 0,1 . 3 = 0,3 mol

Theo (1): nHCl (1) = 2nCuO = 2x 

Theo (2): nHCl (2) = 2nZnO = 2y      

nHCl = 2x + 2y = 0,3                                                                  (**)

Từ (*) và (**) → x = 0,05; y = 0,1

%mCuO=0,05.8012,1.100%=33,06%%mZnO=100%−33,06%=66,94%%mCuO=0,05.8012,1.100%=33,06%%mZnO=100%−33,06%=66,94%

c) CuO + H2SO4 → CuSO4 + H2O

    0,05  →  0,05   

   ZnO + H2SO4 → ZnSO4 + H2O

    0,1  →  0,1

nH2SO4 = 0,05 + 0,1 = 0,15 mol

mH2SO4 = 0,15 . 98 = 14,7g

mdd H2SO4 = 14,7 : 20% = 73,5(g)   

cho mik xin 1 like zới đc khum:))

1, A

2, A

3, B

4, B

5, A

6, C

7, A

8, B

9, A

10, B

11, C

12, D

Bài 7: 

Ta có: \(C=\dfrac{4+\sqrt{7}}{3\sqrt{2}+\sqrt{4+\sqrt{7}}}+\dfrac{4-\sqrt{7}}{3\sqrt{2}-\sqrt{4-\sqrt{7}}}\)

\(=\dfrac{\sqrt{2}\left(4+\sqrt{7}\right)}{6+\sqrt{8+2\sqrt{7}}}+\dfrac{\sqrt{2}\left(4-\sqrt{7}\right)}{6-\sqrt{8-2\sqrt{7}}}\)

\(=\dfrac{\sqrt{2}\left(4+\sqrt{7}\right)}{7+\sqrt{7}}+\dfrac{\sqrt{2}\left(4-\sqrt{7}\right)}{7-\sqrt{7}}\)

\(=\dfrac{\sqrt{2}\left(\sqrt{7}-1\right)\left(4+\sqrt{7}\right)}{6\sqrt{7}}+\dfrac{\sqrt{2}\left(\sqrt{7}+1\right)\left(4-\sqrt{7}\right)}{6\sqrt{7}}\)

\(=\dfrac{\sqrt{2}\left(-3+3\sqrt{7}+3+3\sqrt{7}\right)}{6\sqrt{7}}\)

\(=\sqrt{2}\)

6.

Ta có:

\(A=\sqrt{20+\sqrt{20+...+\sqrt{20}}}>\sqrt{20+\sqrt{\dfrac{1}{16}}}=\dfrac{9}{2}\)

\(B=\sqrt[3]{24+\sqrt[3]{24+...+\sqrt[3]{24}}}>\sqrt[3]{24}=\sqrt[3]{\dfrac{192}{8}}>\sqrt[3]{\dfrac{125}{8}}=\dfrac{5}{2}\)

\(\Rightarrow A+B>\dfrac{9}{2}+\dfrac{5}{2}=7\)

\(A=\sqrt[]{20+\sqrt[]{20+...+\sqrt[]{20}}}< \sqrt[]{20+\sqrt[]{20+...+\sqrt[]{25}}}=5\)

\(B=\sqrt[3]{24+\sqrt[3]{24+...+\sqrt[3]{24}}}< \sqrt[3]{24+\sqrt[3]{24+...+\sqrt[3]{27}}}=3\)

\(\Rightarrow A+B< 5+3=8\)

8.

Ta có:

\(a=\dfrac{1}{2}\sqrt{\sqrt{2}+\dfrac{1}{8}}-\dfrac{\sqrt{2}}{8}\Rightarrow\dfrac{1}{2}\sqrt{\sqrt{2}+\dfrac{1}{8}}=a+\dfrac{\sqrt{2}}{8}\)

\(a^2=\dfrac{1}{4}\left(\sqrt{2}+\dfrac{1}{8}\right)+\dfrac{1}{32}-\dfrac{\sqrt{2}}{4}.\dfrac{1}{2}\sqrt{\sqrt{2}+\dfrac{1}{8}}\)

\(=\dfrac{\sqrt{2}}{4}+\dfrac{1}{32}+\dfrac{1}{32}-\dfrac{\sqrt{2}}{4}\left(a+\dfrac{\sqrt{2}}{8}\right)\)

\(=\dfrac{\sqrt{2}}{4}+\dfrac{1}{16}-\dfrac{\sqrt{2}}{4}a-\dfrac{1}{16}\)

\(=\dfrac{\sqrt{2}}{4}\left(1-a\right)\)

\(\Rightarrow a^4=\dfrac{1}{8}\left(a^2-2a+1\right)\)

\(\Rightarrow a^4+a+1=\dfrac{1}{8}\left(a^2-2a+1\right)+a+1=\dfrac{1}{8}\left(a+3\right)^2\)

\(\Rightarrow R=a^2+\dfrac{\sqrt{2}}{4}\left(a+3\right)=\dfrac{\sqrt{2}}{4}\left(1-a\right)+\dfrac{\sqrt{2}}{4}\left(a+3\right)=\sqrt{2}\)

 C NHA BN CÂU 45 KO LÀM ĐC

2. There used to have many old buildings 10 years ago

3. I wish a new mall didn't build

4. I have had this wardrobe since my wedding day

5. She hasn't been seen for two years

2. There used to be many old buildings 10 years ago.

3. I wish a new mall weren't built here.

4. I have bought this wardrobe since my wedding day.

5. She hasn't been seen (by me) for two years.

1.

\(\Leftrightarrow\sqrt{2}sin\left(x-\dfrac{\pi}{4}\right)=0\)

\(\Leftrightarrow sin\left(x-\dfrac{\pi}{4}\right)=0\)

\(\Leftrightarrow x-\dfrac{\pi}{4}=k\pi\)

\(\Leftrightarrow x=\dfrac{\pi}{4}+k\pi\)

2.

\(\Leftrightarrow\sqrt{2}sin\left(x+\dfrac{\pi}{4}\right)=1\)

\(\Leftrightarrow sin\left(x+\dfrac{\pi}{4}\right)=\dfrac{\sqrt{2}}{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{\pi}{4}=\dfrac{\pi}{4}+k2\pi\\x+\dfrac{\pi}{4}=\dfrac{3\pi}{4}+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=k2\pi\\x=\dfrac{\pi}{2}+k2\pi\end{matrix}\right.\)

3.

\(\Leftrightarrow\left(sin^2x+cos^2x\right)^2-2sin^2x.cos^2x=\dfrac{5}{8}\)

\(\Leftrightarrow1-\dfrac{1}{2}sin^22x=\dfrac{5}{8}\)

\(\Leftrightarrow1-\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{2}cos4x\right)=\dfrac{5}{8}\)

\(\Leftrightarrow\dfrac{3}{4}+\dfrac{1}{4}cos4x=\dfrac{5}{8}\)

\(\Leftrightarrow cos4x=-\dfrac{1}{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}4x=\dfrac{2\pi}{3}+k2\pi\\4x=-\dfrac{2\pi}{3}+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{6}+\dfrac{k\pi}{2}\\x=-\dfrac{\pi}{6}+\dfrac{k\pi}{2}\end{matrix}\right.\)

4.

\(\Leftrightarrow\left(sin^2x+cos^2x\right)^3-3sin^2x.cos^2x\left(sin^2x+cos^2x\right)=\dfrac{1}{4}\)

\(\Leftrightarrow1-\dfrac{3}{4}sin^22x=\dfrac{1}{4}\)

\(\Leftrightarrow1-\dfrac{3}{4}\left(\dfrac{1}{2}-\dfrac{1}{2}cos4x\right)=\dfrac{1}{4}\)

\(\Leftrightarrow cos4x=-1\)

\(\Leftrightarrow4x=\pi+k2\pi\)

\(\Leftrightarrow x=\dfrac{\pi}{4}+\dfrac{k\pi}{2}\)