1 + 1

1/3

N[78945689784528/215487986534]

Sin[78945689784528/215487986534]

InverseLaplaceTransform

prvnipomocnyvypocet

prvnipomocnyvypocet = (a + (b^2))/(((a + b))^2)

hruska jablko

jan_hruska

2  ovadi

1  kyncl

((-b + (Sqrt[(b^2) - 4  a*c]))/(2  a))

??  hruska

hruska = 15
hruska == 15
hruska == 14

Solve[(x^2) + 2  b x + c == 0,  x]
Solve[(x^2) + 2  b x + c == 0,  b]
Solve[(x^2) + 2  b x + c == 0,  c]

?Plot

Plot[{(((x + 1))^2), (((x - 1))^2), Sin[x]}, {x, -2, 
          3}];

Plot[{(((x + 1))^2), (((x - 1))^2), Sin[x]}, {x, -2, 
          3}];

mnozina = {hruska,  jabka,  1,  Pi,  (((x + 1))^2), 
        Sin, ∞,  {1, 2, 3}}

mnozina[[1]]
mnozina[[2]]
mnozina[[-1]]
mnozina[[-1]][[2]]

?List

vektor1 = {1, 2, 3}
vektor2 = {-1, 2, 3}
vektor3 = {1, -2, 3}
matice = {vektor1, vektor2, vektor3}
matice // MatrixForm

Cross[vektor1, vektor2]

{1, 2, 3} . {x, y, z}

Det[matice]
Eigenvalues[matice] // N

mno = Take[mnozina, {1, -3}]
mno . mno

mnozina . mnozina

tabulka = 
        Table[{i, Prime[i]}, {i, 100000}];
ListPlot[tabulka]

Plot[{Cos[x], Sin[x]}, {x, 0, 2  Pi}, 
      PlotStyle -> {{Hue[0], Thickness[ .03]}, {Hue[0.5], 
            Thickness[0.005]}}]

n = 10;
listmocnin = Table[(x^i), {i, 1, n}];
listbarev = 
        Table[{Hue[((i - 1)/n)], Thickness[0.01*1]}, {i, 1, 
            n}];

\(Plot[Evaluate[listmocnin], {x, 0, 1}, PlotRange -> All, 
      AxesLabel -> {"x", \*""\!\(x\^i\)""}, 
      PlotStyle -> listbarev]\)

n = 5;
dvojicekorenu = 
      Table[{Random[Integer, {-10, 10}], 
          Random[Integer, {-10, 10}]}, {n}]
listrovnic = 
      Table[(x - dvojicekorenu[[i, 1]])*(x - 
              dvojicekorenu[[i, 2]]), {i, n}]

dvojicekorenu[[3, 2]]

listrovnic = 
      Table[(x - dvojicekorenu[[i, 1]])*(x - 
              dvojicekorenu[[i, 2]]), {i, n}]

rovnice = 
        a (x^2) + b x  +  c == 0;
reseni = Solve[rovnice, x];
pravidloProKoren1 = reseni[[1]]
pravidloProKoren2 = reseni[[2]]
Simplify[rovnice /. pravidloProKoren1];
Simplify[rovnice /. pravidloProKoren2];
koren1 = x /. pravidloProKoren1
koren2 = x /. pravidloProKoren2
Simplify[koren1 + koren2]
Simplify[koren1*koren2]

pravidloProKoren1
x /. pravidloProKoren1

pravidlo = b -> 5
x /. pravidlo
b /. pravidlo

x + x^2 /. x -> 5

rce = 
      Log[Sin[x]]^2 + 5  Log[Sin[x]] - 3 == 
        0
pravidloSubstituce = Log[Sin[x]] -> z
rce /. pravidloSubstituce
Solve[%, z]
% /. z -> Log[Sin[x]]

rovnice = 
        a (x^2) + b x  +  c == 0;
Solve[rovnice, x]
Simplify[rovnice /. %[[1]]]

dosadzaresenidr = NDSolve[{y'[x] + y[x] == Sin[x], 
            y[0] == 1}, 
          y[x], {x, 0, 1}][[1]]
Plot[y[x]^2 /. dosadzaresenidr, {x, 0, 1}, 
      PlotRange -> All]

{y[x] -> -(1/2) (E^(-x)) (-3 + (E^x) Cos[x] - (E^x) Sin[x])}

FindRoot[x == Cos[x], {x, 1}]

{x, y} /. 
      N[Solve[{x + 3  (y^2) == 1, (x^2) - 5  y == 2}, {x, 
            y}]]

Plot3D[Sin[x y], {x, 0, 4}, {y, 0, 4}, 
        AxesLabel -> {"x", "y", "Sin[x y]  "}, 
        PlotPoints -> 100];

<< Graphics`ImplicitPlot`
<< Graphics`Graphics`

dosadzay2[0]

y1[10]

y /. {y -> (Sqrt[(3/2)])}

ClearAll[y1, y2, dosadzay1, dosadzay2, derivacey1, 
        derivacey2];
rcekuzelosecky = 
        x^2 + 2*x*y + 2 y^2 == 
          3;
dosadzay1[
          x_] = Solve[rcekuzelosecky, 
            y][[1]];
dosadzay2[
          x_] = Solve[rcekuzelosecky, 
            y][[2]];
y1[x_] = 
        y /. dosadzay1[x];
y2[x_] = 
        y /. dosadzay2[x];
doszadery=Solve[D[rcekuzelosecky /. y -> y[x], x],y'[x]][[1]];
derivacey1[x_]=y'[x]/.doszadery/.y[x] -> y1[x];
derivacey2[x_]=y'[x]/.doszadery/.y[x] -> y2[x];
rovnicetecny1[x0_] = 
        y - y1[x0] == 
          derivacey1[
              x0]*(x - x0);
rovnicetecny2[
          x0_] = y - y2[x0] == derivacey2[x0]*(x - x0);

ClearAll[plot1, plot2, plot3];
plot1 := 
      ImplicitPlot[rcekuzelosecky, {x, -3, 3}, 
        PlotRange -> {{-3, 3}, {-2, 
              2}}]
plot2[x0_] := 
      ImplicitPlot[rovnicetecny1[x0], {x, -3, 3}, 
        PlotRange -> {{-3, 3}, {-2, 
              2}}]
plot3[x0_] := 
      ImplicitPlot[rovnicetecny2[x0], {x, -3, 3}, 
        PlotRange -> {{-3, 3}, {-2, 
              2}}]

Do[Print["x0=   ", x0, "   ", 
        rovnicetecny1[x0]], {x0, -2. , 2, 1}]

(Sqrt[5.])  + (Sqrt[7])

ClearAll[f];
f[x_] := (x^2);
f[t + x]
f[x]

(1/3) + 0.

resxy = Solve[{2  x + 3  y - 5  z + 5 == 0, 
            8  x + 2  y - 6  z + 1 == 0}, {x, 
            y}][[1]]
polohovy[z_] = {x /. resxy, y /. resxy, z}
ParametricPlot3D[polohovy[z], {z, -1, 1}, 
      ViewPoint -> {0.513,  -2.760,  1.889}]

ParametricPlot3D[{Cos[t], Sin[t], 0.1  t}, {t, 0, 60  Pi}, 
      PlotPoints -> 5000]