Kennslubókin kafli 4 - Menntaskólinn við HamrahlÃð
Kennslubókin kafli 4 - Menntaskólinn við HamrahlÃð
Kennslubókin kafli 4 - Menntaskólinn við HamrahlÃð
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viii<br />
SVÖR VIÐ ÆFINGUM<br />
Æfing 6.1.1<br />
Dæmi 2.<br />
(a)y=x− 1 2 cos(2x)+k (b)y= 3ln|x2 +x|+k<br />
(c)y= 1 5 (2x5/2 +3) (d)y= ln<br />
∣ (x+1)(x−1)<br />
∣<br />
3<br />
∣+4<br />
(e)y= 1 2 sin(x2 )+k<br />
(f)y=x 2 sin(2x)+xcos(2x)− 1 2 sin(2x)+k.<br />
Æfing 6.2.1<br />
Dæmi 1.<br />
(a)y=k(x+1) (b)y=ke x2 /2 −1 (c)(y+1) 2 =x 2 +k<br />
(d)y= ln ( sin(x)−xcos(x)+k )<br />
Dæmi 2.(3−y) 2 =<br />
Dæmi 3.<br />
k<br />
|2x+1|<br />
1<br />
1−y =ex +k<br />
Sérlausn:y= 3−<br />
Sérlausn:y= 1−e −x<br />
√<br />
3<br />
2x+1 , x>−1/2<br />
Dæmi 4. ln|y|=− 1 x −ln|x|+k Sérlausn:y=x−1 e 1−x−1 , x> 0<br />
Æfing 6.3.1<br />
Dæmi 1.<br />
(a)y= 2x5 −15x 2 +k<br />
10x<br />
(b)y= 3x5 +10x 3 +k<br />
15x 2<br />
(c)y= sin(2x)−2xcos(2x)+k<br />
4x 3<br />
(d)y=e x2 +ke x2 /2<br />
Sérlausn:y=e x2 +4e x2 /2<br />
(e)y= k−3e−sin(x)<br />
cos(x)<br />
Sérlausn:y= 7−3e−sin(x)<br />
cos(x)<br />
Dæmi 2.y=x 2 +kx 2 e x−1 Sérlausn:y=x 2 (1−e x−1 −1 )