Kennslubókin kafli 4 - Menntaskólinn við HamrahlÃð
Kennslubókin kafli 4 - Menntaskólinn við HamrahlÃð
Kennslubókin kafli 4 - Menntaskólinn við HamrahlÃð
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vi<br />
SVÖR VIÐ ÆFINGUM<br />
Dæmi 3.<br />
(a) 40√ 5<br />
3<br />
Dæmi 4.<br />
(b)π 625<br />
12<br />
(a)f er kúrfanC 2 ogg er kúrfanC 1 .<br />
(b)A=(1,0) ogB=(3,3ln(3))<br />
(c) 9ln2 (3)<br />
− 9ln(3) +2<br />
( 2 2 )<br />
2864<br />
(d)π<br />
27 −48ln(3)−36ln2 (3)<br />
Æfing 5.1.2<br />
Dæmi 1.<br />
(a) 36 (b) 32 (c) 216<br />
(d) 69 (e) 104 (f) 92<br />
Dæmi 2.<br />
4∑<br />
(a)<br />
(d)<br />
k=1<br />
k 2<br />
6∑<br />
(k 2 +k) (e)<br />
6∑<br />
(b) (2k+1)<br />
k=1<br />
k=0<br />
k=1<br />
6∑<br />
(k+3)<br />
(c)<br />
(f)<br />
4∑<br />
(2+k 2 )<br />
k=1<br />
7∑<br />
(k 2 +k)<br />
k=1<br />
Dæmi 3.<br />
(a) 1·4+2·5+3·6+···+(n−1)·(n+2)+n·(n+3)<br />
(b) 1·2 1 +2·2 2 +3·2 3 +···+(n−1)·2 n−1 +n·2 n<br />
1<br />
(c)<br />
1·2 + 1<br />
2·3 + 1<br />
3·4 +···+ 1<br />
n·(n+1) + 1<br />
(n+1)·(n+2)<br />
Æfing 5.2.1<br />
Dæmi 1. (a) 2/4,4/7,6/10. (b) 1/2,1/5,1/10. (c) 1,2/3,4/9.<br />
Dæmi 2. (a) 1/243,1/729,1/2187. (b) 1/32,1/64,1/128.<br />
Dæmi 3. (a)a n =<br />
1<br />
2n−1 . (b)a n= 1<br />
3n .<br />
Dæmi 4. (a) 2,4/3,8/9,16/27,32/81. (b) 1,1,2,3,5. (c) 2,2,2,2,2.<br />
Æfing 5.2.3<br />
Dæmi 1. a 1 =−25
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