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

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