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MAT-10352 Insinöörimatematiikka B5 - 18.05.2007

Exam text content

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Original exam

MAT-10355 INSINÖÖRIMATEMATIIKKA E5.
TENTTI 18.05.2007. (Pirttimäki).

 

 

1. Olkoon f(x, y) =x-y ja
0=|(x, y) |0< x, 0< yx+y<2).
Laske Jf| f(x yjdäja [f f(x, y)dal .
O o
2. Olkoon A joukko, jota rajoittavat suorat X + y = 1,
+ y=2 X = 0, y = 0.
Laske

2
[ X"Yi da
X+y
Ohje: Suorita muuttujanvaihto (u=x-y, v=...) ja käytä
kaavaa 1 kaavakokoelmasta.

3. (1) Ratkaise yo fys dx
X
(ii) Ratkaise alkuarvoprobleema yl0=3, y(0)=2

x

y"-2y'+y=-xe

4. Ratkaise ;kun x(0)

1
w

K y(0)=4

y'=5x+4y

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