Mathe:Abschluss 2004-07-27 Brunner

1.

a) [a + bi]p = {x+yi | |y| = |b|}

b) [0]p = relle Zahlen

c) 1 ÄK, in Zahlenebene: 2 Gerade: y = i und y = -i

2.

lim f(x) für x -> 0 = - 1/2

3.

A_n(b) = (b^(n+1)-1)/(12n+12) + ln(b)

A_n(b) = b^(n+1) / 24 + ln(b) - 1/24 (ist das falsch?)

A_3(2) = ln(2) + 7/24

4. eine Variante:

a) E1=(1,0,0)+s(1,1,1)+t(1,0,0)

E2=(1,0,0)+s(1,1,1)+t(0,0,1)

b) n1=(0,sqrt(0.5),-sqrt(0.5))

n2=(sqrt(0.5),-sqrt(0.5),0)

5.

a) (i) det = 1 -> Rang = 3

(ii) -> kein b, wofür nicht lösbar

b) (i) (0,0,0)^ T, (1,1,1)^T, (2,2,2)^ T

(ii) rg(A) = 2 < 3 = rg(A b)

6. a)

fx = cos(x) + cos(x+y)

fy = cos(y) + cos(x+y)

fxx = -sin(x) - sin(x+y)

fyy = -sin(y) - sin(x+y)

fxy = -sin(x+y)

b)

P(PI/3, PI/3) -> rel. Max.

7.

a) y' = -1

b) yh = C2 / x^2 yp = x^3 / 5 + C3 / x^2

y = yh + yp

8.

Int.: 2x^4 - 10x^2 + 8

App.: -8/7x^2 + 136/35

9.

EW = 6/7

p = 10/343