Lösungen/Solutions/
B2S2Ue/Ex14

L = Lektion/ Leçon   -- Sprechstunde / heures de consultation
W = Work / Arbeit / Travail
A  =Anhang/  Annexe / Appendice

Probl/Ex 1      W

s[x_] := 40^2 - 4  x^2;

D[s[x], x] == 0

Solve[D[s[x], x] == 0, {x}]

Plot[s[x], {x, 0, 20}];

v[x_] := (40 - 2  x) x;

D[v[x], x] == 0

Solve[D[v[x], x] == 0, {x}]

Plot[v[x], {x, 0, 20}];

Probl/Ex 2      W

A[x_] :=  2  x (1 - x^2) // Expand

D[A[x], x] == 0

Solve[D[A[x], x] == 0, {x}]

N[%]

Plot[A[x], {x, 0, 1}];

u[x_] :=  2 (2  x  + (1 - x^2)) // Expand

D[u[x], x] == 0

Solve[D[u[x], x] == 0, {x}]

Plot[u[x], {x, 0, 1}];

Probl/Ex 3      W

f[x_] := a x^n;  f[x]

A1[t_] := Integrate[f[x], {x, 0, t}];  A1[t]

A1[x]

A2[x_] := x f[x]  -  A1[x] // Together;  A2[x]

A2[x]/A1[x]

Probl/Ex 4      W

f[x]=a x (x0 - x)

Remove[f]

f[x_] := a x (x0 - x)  //  Expand;  f[x]

A[t_] := Integrate[f[x], {x, 0, t}];  A[x0]

D[f[x], x]

g[x_] := -5/9 x  +  5

cond1 = (f[x1] == g[x1])

cond2 = (D[f[x1], x1] == D[g[x1], x1])

solv = Solve[{cond1, cond2}, {x0, x1}]

res =  A[x0]  /.  solv[[2]]

Plot[res, {a, 0, 2}];

D[res, a] == 0

solv4 = Solve[D[res, a] == 0, a] // Flatten

N[%]

Plot[res, {a, 0.015, 0.016}];

Plot[res, {a, 0.243, 0.25}];

x0 = x0  /.  solv[[2]];  f[x]

a = a  /.  solv4[[2]];   f[x]

Plot[{f[x], g[x]}, {x, 0, 9}];

Probl/Ex 5      W

Remove[f, a, b, c, p]

p[x_] :=  a x (Pi - x) //  Expand; p[
      x]

cond = (
Integrate[p[x], {x, 0, Pi}] == 
          Integrate[Sin[x], {x, 0, Pi}]
)

solv5 = Solve[cond, {a}] // Flatten

a = a /. solv5

p[x]

p[Pi/2]

N[%]

Plot[{p[x], Sin[x]}, {x, 0, Pi}];