Plot[{1 + x - x^2/2,  E^x},  {x,  -1,  1}]

Plot[Sqrt[1 - 2  x^2],  {x,  -Sqrt[2]/2,  Sqrt[2]/2},  
      AspectRatio -> Automatic]

Plot[{Sqrt[1 - 2  x^2],  -Sqrt[1 - 2  x^2]},  {x,  -Sqrt[2]/
          2,  Sqrt[2]/2},  AspectRatio -> Automatic]

ParametricPlot[{Cos[t]/Sqrt[2],  Sin[t]},  {t,  0,  2  Pi},  
      AspectRatio -> Automatic]

v = {-200/7,  Pi,  E,  I}

N[v,  8]

v = v v[[4]]

Integrate[Cos[x],  x]

Limit[Log[1 + x]/x,  x -> 0]

k!!

(k!)!

(* 
      Un modo per vederlo è controllare la forma estesa,  
      usando il comando FullForm che vederemo il prossimo tutorato *)

FullForm[k!!]

FullForm[(k!)!]

?Factorial

?Factorial2

4!!

(4!)!

5!!

(5!)!

Sum[x^k/k!,  {k,  0,  Infinity}] - 1 - x

FullSimplify[
      Sum[x^k/k!,  {k,  0,  Infinity}] - 1 - x]

Sum[x^k/k!,  {k,  2,  Infinity}]

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

Sin[0 + Pi/2]

Cos[0]

D[Sin[x + Pi/2] - Cos[x]]

Simplify[Sin[x + Pi/2]]

Simplify[Sin[x + Pi/2] - Cos[x]]

Simplify[Sin[x + Pi/2],  Cos[x]]

Sum[E^(-c) c^k/k!,  {k,  0,  Infinity}]

Sum[
      Binomial[n,  k] p^k (1 - p)^(n - k),  {k,  0,  
        Infinity}]

FullSimplify[
      Sum[Binomial[n,  k] p^k (1 - p)^(n - k),  {k,  0,  
          Infinity}]]

Plot3D[x^2 + y^2,  {x,  -2, 2},  {y,  -2, 2},  
      AxesLabel -> "Funzione di due variabili"]

Plot3D[
      Sqrt[1 - x^2 - y^2], {x,  -1,  1}, {y,  -1,  1}]

Table[
      Plot3D[Sqrt[1/i^2 - x^2 - y^2], {x,  -1/i,  
          1/i}, {y,  -1/i,  1/i}], {i, 10}]

Solve[x == x^2, x]

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