(* zadacha 1 *)
N[Limit[(((1+(1/n)))^n),n->∞],15]

(* zadacha 2 *)
P[x_]:=(x^5)-5(x^3)-5(x^2)+1;
Factor[P[x]]

P'[x]

Plot[{P[x],P'[x]},{x,-3,1}]

(* zadacha 3 *)
f[x_]:=Sin[(x^2)];
FindRoot[f[x]==(x^3),{x,-π,π}]

Limit[((f[x]-(x^2))/(x^6)),x->0,Direction->-1]

Limit[((f[x]-(x^2))/(x^6)),x->0,Direction->1]

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

(* zadacha 4 *)
A=Table[Table[(i^2)(j+1),{j,1,4}],{i,1,4}];
MatrixForm[A]

Det[A]

Eigensystem[A]

NullSpace[A]