Lista 05 - Minerva.ufpel.tche.br - Universidade Federal de Pelotas

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Respostas:<br />1. (a) 1 + x + x 2 (d)<br />(b) 1 + 2x 3 + 3x 4 (e)<br />(c) 2x 3 + 1<br />1 − x<br />(f)<br />1<br />− 1 − x (g)<br />1 − x<br />x<br />1 − x 2<br />4x<br />1 − x 2<br />1<br />1 + x<br />(h) e −x<br />(i) e 2x<br />2. (a) (1, 4, 6, 4, 1) (g) (1, 0, −1, 0, 1, 0, −1, 0, ...)<br />(b) 1, 2, 1<br />2!<br />, 1<br />3!<br />1 1 , , ... , ...<br />4! k!<br />(h) (1, 2, 1<br />2!<br />, − 1<br />3!<br />, 1<br />4!<br />, − 1<br />5!<br />(c) (0, 0, 1, 3, 3 2 , 3 3 , 3 4 , ....) (i) (0, 0, 0, 1, 4, 4 2 , 4 3 , 4 4 , ...)<br />(d) (2, 0, 1, 0, 1, 0, 1, 0, ...) (j) (1, − 2<br />1!<br />(e) (1, 3, 3, 23<br />3!<br />, 24<br />4!<br />(f) (0, 0, 1, 1, 1<br />2!<br />, 1<br />3!<br />, 25<br />5!<br />, ...) (k) (1, 0, 1<br />2!<br />1 , , ...) (l)<br />4!<br />3. 1 para n = 6 e 462 para n = −6.<br />4. C 9 14.<br />5. 140.<br />6. 10.<br />7. f(x) = (1 − x3 )(1 − x4 )<br />(1 − x) 4 .<br />8. f(x) = 1<br />·<br />1 − x2 1<br />·<br />1 − x3 9. C 13<br />16 − 4C 7 10 + 6C 1 4 = 104.<br />10. 15.<br />11. C r n se n ≥ r e 0 se n < r.<br />12. 6.<br />13. 2 n−1 , n par.<br />1<br />·<br />1 − x4 14. (a) 56. (b) 186480.<br />1<br />.<br />1 − x5 q<br />0<br />, 22<br />2!<br />, − 23<br />3!<br />, 0, 1<br />4!<br /><br />,<br /> q<br />1<br />, 1<br />6!<br />24 , , ...) 4!<br />, 0, 1<br />6!<br />15. (a) 1 + x x2<br />+<br />1! 2! . (b) e3x . (c) ex − e−x .<br />16.<br />1<br />1 − 2x ·<br />1<br />1 − x .<br />17. 4r + 2r+1 .<br />4<br />4<br /><br />,<br />1 , − , ...) 7!<br />1 , 0, , ...) 8!<br /> q<br />2<br /> <br />q<br />, ...<br />q
18. 52.<br />19.<br />4<br />i=1<br />20. 3r + 1<br />.<br />2<br />1<br />.<br />1 − x2i−1 21. (a) é o número de partições de 12 em partes pares.<br />(b) é o número de partições de 15 em partes restritas ao conjunto {3, 6, 9}.<br />22. (a) 11. (b) 5.<br />23. (a) (1+x 6 +x 12 +x 18 +x 24 +x 30 )(1+x 8 +x 16 +x 24 +x 32 )(1+x 10 +x 20 +x 30 )(1+x 20 ).<br />(b) (1 + x 3 + x 6 + x 9 + x 12 )(1 + x 4 + x 8 + x 12 )(1 + x 5 + x 10 )(1 + x 6 + x 12 )(1 + x 7 )<br />(1 + x 8 )(1 + x 9 )(1 + x 10 )(1 + x 11 )(1 + x 12 )(1 + x 13 ).<br />(c) (1 + x)(1 + x 3 )(1 + x 5 )(1 + x 7 )(1 + x 9 )(1 + x 11 ).<br />24. qr(n) · qk(m).<br />25. 4.<br />5
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Lista 05 - Minerva.ufpel.tche.br - Universidade Federal de Pelotas

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