N[Pi]

N[Pi, 1000]

Integrate[1/x, {x, 1, 2}]

N[Integrate[1/x, {x, 1, 2}]]

NIntegrate[1/x, {x, 1, 2}]

Solve[x^3 + x + 1 == 0, x]

%[[1]]

%[[1]]

%^2

x  /.  %8

x1 = x /.  %8

x1

x1^2

x1^3 + x1 + 1

Expand[%]

Simplify[%]

x2 = N[x1]

x2^3 + x2 + 1

Solve[x^5 + 5  x^2 + x + 1 == 0, x]

x1 = x /.  %[[1]]

x1^2

N[x1]

x1

N[x1]

NSolve[x^5 + 5  x^2 + x + 1 == 0, x]

DSolve[{y''[x] + y[x] == 0, 
        y[0] == 2, y'[0] == 3}, y[x], x]

sol = 
      NDSolve[{y''[x] + y[x] == 0, 
          y[0] == 2, y'[0] == 3}, 
        y[x], {x, 0, Pi}]

sol

y[0]  /.  sol

y[x]  /.  sol

%  /.  x -> 1

f[t_] := ((y[x]  /.  sol) /.  
            x -> t)[[1]]

f[1]

Plot[f[x], {x, 0, Pi}]

Plot[Evaluate[y[x]  /. sol], {x, 0, Pi}]

g[t_] := ((y'[x]  /.  sol) /.  
            x -> t)[[1]]

Options[NDSolve]

sol1 = 
      NDSolve[{y''[x] + y[x] == 0, 
          y[0] == 2, y'[0] == 3}, y[x], {x, 0, Pi}, 
        WorkingPrecision -> 32]

y[x]  /.  sol1  /.  x -> 1

NSolve[Sin[x] == x/2, x]

FindRoot[Sin[x] == x/2, {x, Pi}]

Plot[Sin[x] - x/2, {x, -Pi, 2  Pi}]

Plot[x^2 + 100  Sin[x], {x, -10, 10}]

FindMinimum[x^2 + 100  Sin[x], {x, -2}]

sol2 = 
      NDSolve[{y''[x] + x y[x] == 0, 
          y[0] == 0, y'[0] == 1}, y, {x, 0, 10}]

Plot[Evaluate[y[x]  /.  sol2], {x, 0, 10}]

f[x_] := (y[x]  /.  sol2)[[1]]

f[1]

Plot[f[x], {x, 0, 10}]

Plot[Exp[x] + x, {x, -5, 5}]

x0 = x /.  FindRoot[Exp[x] + x == 0, {x, -2}]

h[x_] := Exp[x] + x;

d = 10^(-10);
Plot[h[x0 + d x], {x, -1, 1}]

InputForm[x0]

Options[FindRoot]

x0 = 
      x /.  FindRoot[Exp[x] + x == 0, {x, -2}, 
          WorkingPrecision -> 32]