NIntegrate[Floor[Sqrt[x]],  {x, 0, 16}]

Integrate[Abs[x^2 - 1], {x, 0, 2}]

1/Pi Integrate[Sin[x], {x, 0, Pi}]

Integrate[Tan[x]/(x^2 + 1), {x, -1, 1}]

Limit[(Sin[x^2] + Sin[x]^2)/x^2,  x -> 0]

Limit[Sqrt[x^3 - 2  x^2  +  x]/(x - 1),x -> 1,Direction -> 1]

Limit[(x^2 - x) Cos[1/x],  x -> 0]

Limit[((x^2 + 1)^100  -  (a^2 + 1)^100)/(x - a), 
      x -> a]

D[x^3  Cos[x], x]

D[(x^2 + x + 1)/(x^2 - x + 1), x]

Simplify[%]

D[Sqrt[1 + Sqrt[1 + Sqrt[x]]], x]

D[y[x]^3  +  x^2 y[x]^2  -  x == 1, x]

Solve[%, y'[x]]

% /.  {x -> 1,  y[x] -> 1}

y =  1  +  -1/5 (x - 1) // Simplify

\(a[0]\ \  = \ 1; \ a[1]\  = \ 1; 

    a[n_]\  := \ 2  a[n - 1]\  + \ 8  a[n - 2]\)

Table[a[n], {n, 0, 5}]

b[n_]  =  (4^n  +  (-2)^n)/2

Table[b[n], {n, 0, 5}]

2  b[n - 1]  +  8  b[n - 2]  // Simplify

Plot[{1, (x - 1)/(x + 1)},  {x, 0, 20}]

V  =  Pi ((108 - x)/2  Pi)^2 x

D[V, x]

Solve[% == 0]

Plot[V, {x, 0, 108}]

108 - 36

f[x_]  :=  3/5  x^5  -  5  x^3  +  12  x  -  3

Plot[f[x], {x, -3, 3}]

cp  =  Solve[f'[x] == 0,  x]

f[x] /. cp

% // N

ip = Solve[f''[x] == 0, x]

% // N

f[x] /. ip // N