Problem 1

Solve[Tan[x]==2*x,x]

NSolve[Tan[x]==2*x,x]

Plot[{Tan[x],2*x},{x,-3Pi,3Pi}]

Plot[{Tan[x],2*x},{x,-Pi,Pi}]

Plot[{Tan[x],2*x},{x,1.165-.01,1.165+.01}]

FindRoot[Tan[x]==2 x,{x,1}]

?FindRoot

NSolve[{Tan[x]==2*x,x>1,x<8},x]

Solve[Tan[x]==0,x]

Solve[{Tan[x]==0,x>1,x<20},x]

?Plot

Plot[1/(9-x),{x,0,9},Filling->Bottom,PlotRange->{0,10}]