1+1

(Sqrt[5])

(Sqrt[5.])

N[(Sqrt[5])]

N[(Sqrt[5]),100]

(a+b)*(a-b)
Expand[%]

%

c=3;
d=4;
e=c+d;

husa11=11;
11husa+husa

kyncl je vul

r*h*f

?Sin

LaplaceTransform

x=10;
ClearAll[x];
Integrate[(x^10)*Sin[(1/x)],x]

N[Pi]
Pi//N
N@Pi

120!//N

list={1,2,3,4};
Sin[list]

grafik=Plot[(t^3)Sin[5t+0.4],{t,0,10}];

grafik

DSolve[(x^2)*y''[x]+x*y'[x]+y[x]==0,y[x],x]

ClearAll[y]
DSolve[{(x^2)*y''[x]+x*y'[x]+y[x]==0,y'[1]==1,y[1]==-1},y[x],x]
Plot[Evaluate[y[x]/.%], {x,-10,10}]

Plot[-Cos[Log[x]]+Sin[Log[x]],{x,1,10}]

(*zde druhe cviceni*)
Quiet@Remove["Global`*"]

D[Tanh[x],x]
Tanh'[x]

Sin'

Plot[{D[Tanh[x],x],(1/(1+(x^2)))},{x,-5,5},AxesLabel->{"x","fce"},GridLines->Automatic,PlotStyle->{{Black,Thick},{Red,Thick}}]

Plot[{Tanh'[x],(1/(1+(x^2)))},{x,-5,5},AxesLabel->{"x","fce"},GridLines->Automatic,PlotStyle->{{Black,Thick},{Red,Thick}}]

Manipulate[
Plot[{Tanh'[k*x],(1/(1+(x^2)))},{x,-5,5},AxesLabel->{"x","fce"},GridLines->Automatic,PlotStyle->{{Black,Thick},{Red,Thick}}]
,{{k,1},0,2}]

x=5
psi=1

ClearAll[f,g,x,psi];
f[x_]=3*x*Cos[3x];
g[psi_]=((Sin[psi])/(1+(psi^2)));
Plot[g[3*f[(Sqrt[t])+1]],{t,1,10},AxesLabel->{"t","g[3*f[(Sqrt[t])+1]]]"},GridLines->Automatic,PlotStyle->{Magenta,Thick,Dashed}]

ClearAll[f,g];
f[x_]:=3*x*Cos[3x];
g[psi_]:=((Sin[psi])/(1+(psi^2)));
Plot[g[3*f[(Sqrt[t])+1]],{t,1,10},AxesLabel->{"t","g[3*f[(Sqrt[t])+1]]"},GridLines->Automatic,PlotStyle->{Magenta,Thick,Dashed}]

a==b
FullForm[%]

rovnice=(x^3)+(1/(1+(t^2)))*(x^2)+t*x-1==0;
dosadZax123=Solve[rovnice,x];
x1=x/.dosadZax123[[1]];
x2=x/.dosadZax123[[2]];
x3=x/.dosadZax123[[3]];
proPlot=Abs[x1]+Abs[x2]+Abs[x3];
Plot[proPlot,{t,1,10},AxesLabel->{"t","Abs[x1]+Abs[x2]+Abs[x3]"},GridLines->Automatic,PlotStyle->{Blue,Thick}]

x/.Solve[(x^3)==8]

Abs[{a,b,c}]

Plus@@Abs[x/.Solve[(x^3)+(1/(1+(t^2)))*(x^2)+t*x-1==0,x]]//Plot[#,{t,1,10},AxesLabel->{"t","Abs[x1]+Abs[x2]+Abs[x3]"},GridLines->Automatic,PlotStyle->{Blue,Thick}]&

ClearAll[f];
rce=(1+(t^2))*(x^4)+(x/(1+(t^4)))==Sin[1+(t^3)];
dosadZax1234=Solve[rce,x];
x1=x/.dosadZax1234[[1]];
x2=x/.dosadZax1234[[2]];
x3=x/.dosadZax1234[[3]];
x4=x/.dosadZax1234[[4]];
f[t_]=((Abs[x1]-Abs[x4])/(1+Abs[x2]+Abs[x3]));
proPlot=f[3*Cos[1+(x^2)]];
Plot[proPlot,{x,0,5},AxesLabel->{"t","((Abs[x1] - Abs[x4])/(1 + Abs[x2] + Abs[x3]))"},GridLines->Automatic,PlotStyle->{Red,Thick}]

ClearAll[f];
rce=(1+(t^2))*(x^4)+(x/(1+(t^4)))==Sin[1+(t^3)];
dosadZax1234=Solve[rce,x];
x1=x/.dosadZax1234[[1]];
x2=x/.dosadZax1234[[2]];
x3=x/.dosadZax1234[[3]];
x4=x/.dosadZax1234[[4]];
f[t_]:=((Abs[x1]-Abs[x4])/(1+Abs[x2]+Abs[x3]));

proPlot=f[3*Cos[1+(x^2)]];
Plot[proPlot,{x,0,5},AxesLabel->{"t","((Abs[x1] - Abs[x4])/(1 + Abs[x2] + Abs[x3]))"},GridLines->Automatic,PlotStyle->{Red,Thick}]

?f