1: TXĐ là D=R

Khi x∈D thì -x∈D
\(f\left(-x\right)=2\cdot\left(-x\right)+3\left(-x\right)^3\cdot cos\left(-2x\right)=-2x-3x^3\cdot cos2x\)

=-f(x)

=>f(x) là hàm số lẻ

2: ĐKXĐ: sin x<>0

=>\(x<>k\pi\)

=>TXĐ là D=R\{kπ}

Khi x∈D thì -x∈D

\(f\left(-x\right)=\frac{1}{\sin\left(-x\right)}=\frac{-1}{\sin x}=-f\left(x\right)\)

=>f(x) là hàm số lẻ

3: ĐKXĐ: tan x<>0 và \(x<>\frac{\pi}{2}+k\pi\)

=>\(x<>k\pi;x<>\frac{\pi}{2}+k\pi\)

=>\(x<>\frac{k\pi}{2}\)

=>TXĐ là D=R\{\(\frac{k\pi}{2}\) }

Khi x∈D thì -x∈D

\(f\left(-x\right)=\frac{\left.\left(-x\right)^2\right.}{3\cdot\tan\left(-x\right)}=\frac{x^2}{-3\cdot\tan x}=-f\left(x\right)\)

=>f(x) là hàm số lẻ

4: ĐKXĐ: \(3x<>\frac{\pi}{2}+k\pi\)

=>\(x<>\frac{\pi}{6}+\frac{k\pi}{3}\)

=>TXĐ là D=R\{\(\frac{\pi}{6}+\frac{k\pi}{3}\) }

Khi x∈D thì -x∈D

\(f\left(-x\right)=\sin\left(-x\right)+\tan\left(-3x\right)+cos\left(-3x\right)\)

=-sin x-tan 3x+cos3x

=>f(-x)<>-f(x) và f(-x)<>f(x)

=>f(x) không có tính chẵn lẻ

Gọi kim loại cần tìm là R (II)

Gọi \(\left\{{}\begin{matrix}n_{Fe}=a\left(mol\right)\\n_R=b\left(mol\right)\end{matrix}\right.\)

\(\Rightarrow56a+M_R.b=8\left(g\right)\)

\(n_{HCl}=0,2.2=0,4\left(mol\right)\)

PTHH:

Fe + 2HCl --->FeCl₂ + H₂

a---->2a

R + 2HCl ---> RCl₂ + H₂

b---->2b

Theo pthh: \(n_{hhkl}=n_{H_2}=\dfrac{1}{2}n_{HCl}=\dfrac{1}{2}.0,4=0,2\left(mol\right)\)

\(\Rightarrow V_{H_2}=0,2.22,4=4,48\left(l\right)\)

b, Lập được hệ pt: \(\left\{{}\begin{matrix}56a+M_R.b=8\\2a+2b=0,4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=0,1\left(mol\right)\\b=0,1\left(mol\right)\\M_R=24\left(\dfrac{g}{mol}\right)\end{matrix}\right.\)

=> R là Mg

c, \(\left\{{}\begin{matrix}n_{Fe}=0,1\left(mol\right)\\n_{Mg}=0,1\left(mol\right)\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}m_{Fe}=0,1.56=5,6\left(g\right)\\m_{Mg}=0,1.56=5,6\left(g\right)\end{matrix}\right.\)

Quy hết kim loại R (II) và Fe về M (II):

\(n_{HCl}=0,2.2=0,4\left(mol\right)\)

PTHH: M + 2HCl ---> MCl₂ + H₂↑

           0,2<-0,4------->0,2---->0,2

=> V_H2 = 0,2.22,4 = 4,48 (l)

\(b,M_M=\dfrac{8}{0,2}=40\left(\dfrac{g}{mol}\right)\\ \rightarrow M_R=2.40-56=24\left(\dfrac{g}{mol}\right)\)

=> R là Mg

c, Gọi \(\left\{{}\begin{matrix}n_{Fe}=a\left(mol\right)\\n_{Mg}=b\left(mol\right)\end{matrix}\right.\left(a,b>0\right)\)

PTHH:

Fe + 2HCl ---> FeCl₂ + H₂

a---->2a--------->a

Mg + 2HCl ---> MgCl₂ + H₂

b---->2b-------->b

=> hệ pt \(\left\{{}\begin{matrix}56a+24b=8\\2a+2b=0,4\end{matrix}\right.\Leftrightarrow a=b=0,1\left(mol\right)\left(TM\right)\)

=> \(\left\{{}\begin{matrix}m_{Fe}=0,1.56=5,6\left(g\right)\\m_{Mg}=0,1.24=2,4\left(g\right)\end{matrix}\right.\)

d, \(\left\{{}\begin{matrix}C_{M\left(FeCl_2\right)}=\dfrac{0,1}{0,2}=0,5M\\C_{M\left(MgCl_2\right)}=\dfrac{0,1}{0,2}=0,5M\end{matrix}\right.\)

Bài 13:

ĐKXĐ: x∉{0;2;-2;1/2}

a: \(B=\left(\frac{x+2}{2-x}-\frac{4x^2}{x^2-4}-\frac{2-x}{x+2}\right):\frac{2x^2-x}{x^2-2x}\)

\(=\left(\frac{-\left(x+2\right)}{x-2}-\frac{4x^2}{\left(x-2\right)\left(x+2\right)}+\frac{x-2}{x+2}\right):\frac{x\left(2x-1\right)}{x\left(x-2\right)}\)

\(=\frac{-\left(x+2\right)^2-4x^2+\left(x-2\right)^2}{\left(x-2\right)\left(x+2\right)}\cdot\frac{x-2}{2x-1}\)

\(=\frac{-x^2-4x-4-4x^2+x^2-4x+4}{x+2}\cdot\frac{1}{2x-1}=\frac{-4x^2-8x}{\left(x+2\right)\left(2x-1\right)}\)

\(=\frac{-4x\left(x+2\right)}{\left.\left(x+2\right)\left(2x-1\right)\right.}=\frac{-4x}{2x-1}\)
b: |x|=3

=>x=3 hoặc x=-3

Khi x=3 thì \(B=\frac{-4\cdot3}{2\cdot3-1}=\frac{-12}{5}\)

Khi x=-3 thì \(B=\frac{-4\cdot\left(-3\right)}{2\cdot\left(-3\right)-1}=\frac{12}{-6-1}=\frac{-12}{7}\)

c: Để B nguyên thì -4x⋮2x-1

=>-4x+2-2⋮2x-1

=>-2⋮2x-1

mà 2x-1 lẻ

nên 2x-1∈{1;-1}

=>2x∈{2;0}

=>x∈{1;0}

Kết hợp ĐKXĐ, ta được: x=1

Bài 12:

a: ĐKXĐ: a∉{1;-1;-2}

b: \(P=\left(\frac{a+1}{2a-2}+\frac{1}{2-2a^2}\right)\cdot\frac{2a+2}{a+2}\)

\(=\left(\frac{a+1}{2\left(a-1\right)}-\frac{1}{2\left(a-1\right)\left(a+1\right)}\right)\cdot\frac{2\left(a+1\right)}{a+2}\)

\(=\frac{\left(a+1\right)^2-1}{2\left(a-1\right)\left(a+1\right)}\cdot\frac{2\left(a+1\right)}{a+2}=\frac{a\left(a+2\right)}{\left(a-1\right)\left(a+2\right)}=\frac{a}{a-1}\)

c: |a|=2

=>a=2(nhận) hoặc a=-2(loại)

Khi a=2 thì \(P=\frac{2}{2-1}=\frac21=2\)

Bài 11:

a: ĐKXĐ: x∉{2;-3}

b: \(P=\frac{x+2}{x+3}-\frac{5}{x^2+3x-2x-6}+\frac{1}{2-x}\)

\(=\frac{x+2}{x+3}-\frac{5}{\left(x+3\right)\left(x-2\right)}-\frac{1}{x-2}\)

\(=\frac{\left(x+2\right)\left(x-2\right)-5-\left(x+3\right)}{\left(x+3\right)\left(x-2\right)}=\frac{x^2-4-5-x-3}{\left(x+3\right)\left(x-2\right)}\)

\(=\frac{x^2-x-12}{\left(x+3\right)\left(x-2\right)}=\frac{\left(x-4\right)\left(x+3\right)}{\left(x+3\right)\left(x-2\right)}=\frac{x-4}{x-2}\)

c: \(P=\frac{-3}{4}\)

=>\(\frac{x-4}{x-2}=\frac{-3}{4}\)

=>4(x-4)=-3(x-2)

=>4x-16=-3x+6

=>7x=22

=>\(x=\frac{22}{7}\) (nhận)

d: Để P nguyên thì x-4⋮x-2

=>x-2-2⋮x-2

=>-2⋮x-2

=>x-2∈{1;-1;2;-2}

=>x∈{3;1;4;0}

e: \(x^2-9=0\)

=>\(x^2=9\)

=>x=3(nhận) hoặc x=-3(loại)

Khi x=3 thì \(P=\frac{3-4}{3-2}=-1\)

-14/18<0

0<-30/-40=3/4=9/12<9/11

9/11<1<-12/-8

=>-14/18<0<-30/-40<9/11<-12/-8

cảm ơn ah