Problem 1

N[π,768]

Problem 2

N[((((2143/22)))^(1/4)),14]

Problem 3

mp = 938.2723;
me = 0.51109991;
ratio = mp/me

f[n_,m_,p_]:=(2^n) (3^m) (π^p)

f[1,2,4]//N

Do[
If[Abs[f[i,j,k]-ratio]<1,Print["i,j,k= [",i,",  ",j,",  ",k,"]  f=",f[i,j,k]//N]],
{i,1,10},{j,1,10},{k,1,10}]

Problem 4

α=(1/137.0359895);
SetPrecision[1+(∑_(n=1)^5)((((-1))^(n+1))/(n+1)) ((((α/π)))^n),10]

Compared to μ = 1.00115965219 eℏ/2(Subscript[m, e])

Problem 5

seriesTan[x_,nf_]:= 4 ((∑_(n=0)^nf)((((-1))^n)/(2 n +1))(x^(2 n+1)))

Table[seriesTan[1,j]//N,{j,120,121}]

Problem 6

n=12;
pie = N[(4 seriesTan[(1/5),n] -seriesTan[(1/239),n]),20]

Problem 7

z = SetPrecision[(E^(π (Sqrt[163]))),31]

NumberForm[z,ExponentFunction->(Null &)]

Problem 8

(x^5)+8 (x^4)-72 (x^3)-382 (x^2)+727 x+2310==0

Solve[(x^5)+8 (x^4)-72 (x^3)-382 (x^2)+727 x+2310==0,x]

Factor[(x^5)+8 (x^4)-72 (x^3)-382 (x^2)+727 x+2310]

Problem 9

Plot[{x,(E^x)},{x,-2,2}]

Plot[{-x,(E^x)},{x,-2,2}]

FindRoot[-x==(E^x),{x,-0.5}]

Problem 10

h = {2 (Subscript[i, 1]) + 3 (Subscript[i, 2]) - 4 (Subscript[i, 3])==5,3 (Subscript[i, 1]) - 2 (Subscript[i, 2]) + 4 (Subscript[i, 3])==6,4 (Subscript[i, 1]) + (Subscript[i, 2]) - 4 (Subscript[i, 3])==7}

Solve[h,{(Subscript[i, 1]),(Subscript[i, 2]),(Subscript[i, 3])}]