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mathematics 3
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SVEUČILIŠTE J. J. STROSSMAYERA U OSIJEKU
02. rujna 2010.
GRUPA
1.
PISMENI ISPIT IZ MATEMATIKE III
1. Prijelazom na polarne koordinate izračunajte dvostruki integral ‡ ‡ y „ x „ y,
S
a
gdje je S polukrug promjera a sa središtem u točki C
, 0 .
2
2. Naite prirast funkcije f Hx, yL = x3 - 2 y3 + 3 xy pri prijelazu od vrijednosti x = 1,
y = 2 na vrijednosti x1 = 1 + h, y1 = 2 + k.
3. Nacrtajte nivo linije dane funkcije f Hx, yL = H1 + x + yL2 i ispitajte karakter plohe koja odgovara ovoj funkciji.
4. Na plohi x2 + y2 - z2 - 2 x = 0 naite točke u kojima su tangencijalne ravnine na plohu paralelne s koordinatnim osima.
5. Izračunajte ò y2 „ x + x2 „ y gdje je C gornja polovina pozitivno orijentirane elipse sa središtem u
C
ishodištu koordinatnog sustava u ravnini, s velikom poluosi, a = 4, na x - osi i malom, b = 3, na y - osi.
ELEKTROTEHNIČKI FAKULTET
SVEUČILIŠTE J. J. STROSSMAYERA U OSIJEKU
02. rujna 2010.
GRUPA
1.
PISMENI ISPIT IZ MATEMATIKE III
1. Prijelazom na polarne koordinate izračunajte dvostruki integral ‡ ‡ y „ x „ y,
S
a
gdje je S polukrug promjera a sa središtem u točki C
, 0 .
2
2. Naite prirast funkcije f Hx, yL = x3 - 2 y3 + 3 xy pri prijelazu od vrijednosti x = 1,
y = 2 na vrijednosti x1 = 1 + h, y1 = 2 + k.
3. Nacrtajte nivo linije dane funkcije f Hx, yL = H1 + x + yL2 i ispitajte karakter plohe koja odgovara ovoj funkciji.
4. Na plohi x2 + y2 - z2 - 2 x = 0 naite točke u kojima su tangencijalne ravnine na plohu paralelne s koordinatnim osima.
5. Izračunajte ò y2 „ x + x2 „ y gdje je C gornja polovina pozitivno orijentirane elipse sa središtem u
C
ishodištu koordinatnog sustava u ravnini, s velikom poluosi, a = 4, na x - osi i malom, b = 3, na y - osi.
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