Lösungen / Solutions/I1S2Ue/Ex14

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

Ueb/Ex 1      W

a

?Series

Series[Log[x],  {x,  1,  20}]

f[x_] := 
        Evaluate[Normal[Series[Log[u],  {u,  1,  20}]]] /. 
          u -> x;
f[x]

f[y]

f[y] // Expand

f[1]

f[1] // N

b

g[x_] := 
        Evaluate[Normal[Series[1/u,  {u,  1,  20}]]] /. 
          u -> x;
b = g[x]

b = g[x] // Expand

a - b

a - b // Expand

c

?D

a = D[f[x], x]

D[f[x], x] // Expand

d

D[f[x], x] - g[x]

D[f[x], x] - g[x] // Expand

D[f[x], x] - g[x] /. x -> 1

Ueb/Ex 2      W

a

Solve[Sin[x] == Cos[x], {x}]

Solve[Sin[x] == Cos[x], {x}] // N

a = Normal[Series[Sin[x],  {x,  1, 2}]]

a = Normal[Series[Sin[x],  {x,  0, 6}]]

a = Normal[Series[Sin[x],  {x,  0, 2}]] // Expand // N

b = Normal[Series[Cos[x],  {x,  1, 2}]]

b = Normal[Series[Cos[x],  {x,  0, 6}]]

b = Normal[Series[Cos[x],  {x,  0,  2}]] // Expand // 
        N

b

Solve[a == b, {x}]

Solve[a == b, {x}] // N // Chop

Solve[Sin[x] == Cos[x], {x}] // N

c

NSolve[Sin[x] == Cos[x], {x}]

FindRoot[Sin[x] == Cos[x], {x, 1}]