s251ex2(sp08)

s251ex2(sp08) - (a) -= ) 2 cos( 2 ) 2 cos( 2 ) 2 sin( 2 ) (...

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MATH 251 Exam II April 7, 2008 ANSWER KEY 1. A 2, B 3. D 4. B 5. B 6. A 7. ) 4 ( ) ( ) ( ) ) ( 1 ( ) ( 2 5 2 5 t e t u t t u t f - - - - = π - + + + + + - = - - s s s s e e s s s F s 25 10 2 2 4 2 ) ( 2 3 10 5 3 8. + + - - + + - = - + - - + - 24 4 6 6 8 4 2 2 20 1 5 1 4 1 ) ( 20 1 5 1 4 1 ) ( ) ( t t t t e e t u e e t u t y 9. (a) t t e e t x 4 2 12 8 8 8 ) ( - - - + - = (b) It is a node, asymptotically stable (i.e. it is a nodal sink ). 10.
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Unformatted text preview: (a) -= ) 2 cos( 2 ) 2 cos( 2 ) 2 sin( 2 ) ( 3 t t t e t x t (b) It is a spiral point, unstable (i.e. it is a spiral source ). 11. (a) (0,0), (0,-2), (1,-1) (b) It is a saddle point; unstable....
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