f:= Sin[x]-3*Sin[2*x]+2*Cos[3*x]

Plot[f,{x,0,2*Pi}]

g:= D[f,x]

FindRoot[g==0,{x,0,1.5}]

f /. %

FindRoot[g==0,{x,1.5,2.5}]

f /. %

FindRoot[g==0,{x,2.5,4}]

f /. %

FindRoot[g==0,{x,5,6.2}]

f /. %

Limit[x^(1/x),x->Infinity]

NIntegrate[(2+6*x^2+9*x^4)^(1/2),{x,0,1}]

Series[Exp[x]*(Sin[x]+x)/Cos[x],{x,0,6}]

D[Tan[x^2+x*y-y^2],{x,2},y]

f:= x^4+y^4-10*x^2*y-30*x*y-5*x*y^2

g:= D[f,x]

h:= D[f,y]

S:= NSolve[{g==0,h==0},{x,y}]

S

Plot3D[f,{x,-1,1},{y,-1,1}]

Plot3D[f,{x,-1.5,0.5},{y,-1.5,0.5}]

Plot3D[f,{x,6.5,7},{y,6.5,7}]

Plot3D[f,{x,-7,7},{y,-7,7}]

A:= D[g,x]

B:= D[g,y]

F:= D[h,y]

K:= B^2-A*F

K /. S

g:= x^2+y^2+z^2-1

h:= x*y^2-y*z^2+z*x^2

f:= 2*x^2*y+y^2*z-x*z

A:= D[g,x]*D[h,y]-D[g,y]*D[h,x]

B:= D[g,x]*D[h,z]-D[g,z]*D[h,x]

F:= D[g,y]*D[h,z]-D[g,z]*D[h,y]

NSolve[{g==0,h==0,A==0,B==0,F==0},{x,y,z}]

A:= {{D[g,x],D[g,y],D[g,z]},{D[h,x],D[h,y],D[h,z]},
{D[f,x],D[f,y],D[f,z]}}

S:= NSolve[{g==0,h==0,Det[A]==0},{x,y,z}]

S

f /. S

Integrate[Integrate[Integrate[z,{z,0,x^4+y^2}],{y,1,2}],{x,1,2}]