Facit

Sommarmatte 1

(Skillnad mellan versioner)
Hoppa till: navigering, sök
Versionen från 16 juli 2007 kl. 09.26 (redigera)
KTH.SE:u1zpa8nw (Diskussion | bidrag)

← Gå till föregående ändring
Nuvarande version (17 juli 2007 kl. 11.00) (redigera) (ogör)
KTH.SE:u1zpa8nw (Diskussion | bidrag)

 
(10 mellanliggande versioner visas inte.)
Rad 1: Rad 1:
__NOTOC__ __NOTOC__
'''Svar 1.1:1''' '''Svar 1.1:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 18: Rad 18:
</div> </div>
-==Svar 1.1:2==+'''Svar 1.1:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 36: Rad 36:
</div> </div>
-==Svar 1.1:3==+'''Svar 1.1:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left" valign="top"> <tr align="left" valign="top">
Rad 74: Rad 74:
</div> </div>
-==Svar 1.1:4==+'''Svar 1.1:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 92: Rad 92:
</div> </div>
-==Svar 1.1:5==+'''Svar 1.1:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 109: Rad 109:
</div> </div>
-==Svar 1.1:6==+'''Svar 1.1:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 131: Rad 131:
</div> </div>
-==Svar 1.2:1==+'''Svar 1.2:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 151: Rad 151:
</div> </div>
-==Svar 1.2:2==+'''Svar 1.2:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 169: Rad 169:
</div> </div>
-==Svar 1.2:3==+'''Svar 1.2:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
Rad 182: Rad 182:
</div> </div>
-==Svar 1.2:4==+'''Svar 1.2:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 196: Rad 196:
</div> </div>
-==Svar 1.2:5==+'''Svar 1.2:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
Rad 211: Rad 211:
</div> </div>
-==Svar 1.2:6==+'''Svar 1.2:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"><tr><td class="ntext">$\displaystyle \frac{152}{35}$</td></tr></table> <table width="100%"><tr><td class="ntext">$\displaystyle \frac{152}{35}$</td></tr></table>
</div> </div>
-==Svar 1.3:1==+'''Svar 1.3:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 232: Rad 232:
</div> </div>
-==Svar 1.3:2==+'''Svar 1.3:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 246: Rad 246:
</div> </div>
-==Svar 1.3:3==+'''Svar 1.3:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 264: Rad 264:
</div> </div>
-==Svar 1.3:4==+'''Svar 1.3:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 284: Rad 284:
</div> </div>
-==Svar 1.3:5==+'''Svar 1.3:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 306: Rad 306:
</div> </div>
-==Svar 1.3:6==+'''Svar 1.3:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 328: Rad 328:
</div> </div>
-==Svar 2.1:1==+'''Svar 2.1:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 356: Rad 356:
</div> </div>
-==Svar 2.1:2==+'''Svar 2.1:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 378: Rad 378:
</div> </div>
-==Svar 2.1:3==+'''Svar 2.1:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 400: Rad 400:
</div> </div>
-==Svar 2.1:4==+'''Svar 2.1:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 418: Rad 418:
</div> </div>
-==Svar 2.1:5==+'''Svar 2.1:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 436: Rad 436:
</div> </div>
-==Svar 2.1:6==+'''Svar 2.1:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 454: Rad 454:
</div> </div>
-==Svar 2.1:7==+'''Svar 2.1:7'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 468: Rad 468:
</div> </div>
-==Svar 2.1:8==+'''Svar 2.1:8'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 482: Rad 482:
</div> </div>
-==Svar 2.2:1==+'''Svar 2.2:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 500: Rad 500:
</div> </div>
-==Svar 2.2:2==+'''Svar 2.2:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 518: Rad 518:
</div> </div>
-==Svar 2.2:3==+'''Svar 2.2:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 540: Rad 540:
</div> </div>
-==Svar 2.2:4==+'''Svar 2.2:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 555: Rad 555:
</div> </div>
-==Svar 2.2:5==+'''Svar 2.2:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 581: Rad 581:
</div> </div>
-==Svar 2.2:6==+'''Svar 2.2:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 603: Rad 603:
</div> </div>
-==Svar 2.2:7==+'''Svar 2.2:7'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 618: Rad 618:
</div> </div>
-==Svar 2.2:8==+'''Svar 2.2:8'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 633: Rad 633:
</div> </div>
-==Svar 2.2:9==+'''Svar 2.2:9'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 652: Rad 652:
-==Svar 2.3:1==+'''Svar 2.3:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 668: Rad 668:
</div> </div>
-==Svar 2.3:2==+'''Svar 2.3:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 690: Rad 690:
</div> </div>
-==Svar 2.3:3==+'''Svar 2.3:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 714: Rad 714:
</div> </div>
-==Svar 2.3:4==+'''Svar 2.3:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 732: Rad 732:
</div> </div>
-==Svar 2.3:5==+'''Svar 2.3:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 750: Rad 750:
</div> </div>
-==Svar 2.3:6==+'''Svar 2.3:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 764: Rad 764:
</div> </div>
-==Svar 2.3:7==+'''Svar 2.3:7'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 778: Rad 778:
</div> </div>
-==Svar 2.3:8==+'''Svar 2.3:8'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 788: Rad 788:
</div> </div>
-==Svar 2.3:9==+'''Svar 2.3:9'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 802: Rad 802:
</div> </div>
-==Svar 2.3:10==+'''Svar 2.3:10'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 810: Rad 810:
</table> </table>
</div> </div>
-==Svar 3.1:1==+'''Svar 3.1:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 826: Rad 826:
</div> </div>
-==Svar 3.1:2==+'''Svar 3.1:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 852: Rad 852:
</div> </div>
-==Svar 3.1:3==+'''Svar 3.1:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 870: Rad 870:
</div> </div>
-==Svar 3.1:4==+'''Svar 3.1:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 888: Rad 888:
</div> </div>
-==Svar 3.1:5==+'''Svar 3.1:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 904: Rad 904:
</div> </div>
-==Svar 3.1:6==+'''Svar 3.1:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 922: Rad 922:
</div> </div>
-==Svar 3.1:7==+'''Svar 3.1:7'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 936: Rad 936:
</div> </div>
-==Svar 3.1:8==+'''Svar 3.1:8'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 954: Rad 954:
</div> </div>
-==Svar 3.2:1==+'''Svar 3.2:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 963: Rad 963:
</div> </div>
-==Svar 3.2:2==+'''Svar 3.2:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 972: Rad 972:
</div> </div>
-==Svar 3.2:3==+'''Svar 3.2:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 981: Rad 981:
</div> </div>
-==Svar 3.2:4==+'''Svar 3.2:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 990: Rad 990:
</div> </div>
-==Svar 3.2:5==+'''Svar 3.2:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 999: Rad 999:
</div> </div>
-==Svar 3.2:6==+'''Svar 3.2:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 008: Rad 1 008:
</div> </div>
-==Svar 3.3:1==+'''Svar 3.3:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 026: Rad 1 026:
</div> </div>
-==Svar 3.3:2==+'''Svar 3.3:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 052: Rad 1 052:
</div> </div>
-==Svar 3.3:3==+'''Svar 3.3:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 080: Rad 1 080:
</div> </div>
-==Svar 3.3:4==+'''Svar 3.3:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 094: Rad 1 094:
</div> </div>
-==Svar 3.3:5==+'''Svar 3.3:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 116: Rad 1 116:
</div> </div>
-==Svar 3.3:6==+'''Svar 3.3:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%" > <table width="100%" >
<tr align="left"><td height="5px"/></tr> <tr align="left"><td height="5px"/></tr>
Rad 1 135: Rad 1 135:
</div> </div>
-==Svar 3.4:1==+'''Svar 3.4:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 149: Rad 1 149:
</div> </div>
-==Svar 3.4:2==+'''Svar 3.4:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 163: Rad 1 163:
</div> </div>
-==Svar 3.4:3==+'''Svar 3.4:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 179: Rad 1 179:
</div> </div>
-==Svar 4.1:1==+'''Svar 4.1:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 197: Rad 1 197:
</div> </div>
-==Svar 4.1:2==+'''Svar 4.1:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 213: Rad 1 213:
</div> </div>
-==Svar 4.1:3==+'''Svar 4.1:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 227: Rad 1 227:
</div> </div>
-==Svar 4.1:4==+'''Svar 4.1:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 245: Rad 1 245:
</div> </div>
-==Svar 4.1:5==+'''Svar 4.1:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 259: Rad 1 259:
</div> </div>
-==Svar 4.1:6==+'''Svar 4.1:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 275: Rad 1 275:
</div> </div>
-==Svar 4.1:7==+'''Svar 4.1:7'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 295: Rad 1 295:
</div> </div>
-==Svar 4.1:8==+'''Svar 4.1:8'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 305: Rad 1 305:
</div> </div>
-==Svar 4.1:9==+'''Svar 4.1:9'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 315: Rad 1 315:
</div> </div>
-==Svar 4.1:10==+'''Svar 4.1:10'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 324: Rad 1 324:
</div> </div>
-==Svar 4.2:1==+'''Svar 4.2:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
Facit till alla delfrågor<br \> Facit till alla delfrågor<br \>
<table width="100%"> <table width="100%">
Rad 1 349: Rad 1 349:
</div> </div>
-==Svar 4.2:2==+'''Svar 4.2:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 373: Rad 1 373:
</div> </div>
-==Svar 4.2:3==+'''Svar 4.2:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 395: Rad 1 395:
</div> </div>
-==Svar 4.2:4==+'''Svar 4.2:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 417: Rad 1 417:
</div> </div>
-==Svar 4.2:5==+'''Svar 4.2:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 433: Rad 1 433:
</div> </div>
-==Svar 4.2:6==+'''Svar 4.2:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 442: Rad 1 442:
</div> </div>
-==Svar 4.2:7==+'''Svar 4.2:7'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 452: Rad 1 452:
-==Svar 4.2:8==+'''Svar 4.2:8'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 461: Rad 1 461:
</div> </div>
-==Svar 4.2:9==+'''Svar 4.2:9'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 470: Rad 1 470:
</div> </div>
-==Svar 4.3:1==+'''Svar 4.3:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 484: Rad 1 484:
</div> </div>
-==Svar 4.3:2==+'''Svar 4.3:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 496: Rad 1 496:
</div> </div>
-==Svar 4.3:3==+'''Svar 4.3:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 520: Rad 1 520:
</div> </div>
-==Svar 4.3:4==+'''Svar 4.3:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 544: Rad 1 544:
</div> </div>
-==Svar 4.3:5==+'''Svar 4.3:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 553: Rad 1 553:
</div> </div>
-==Svar 4.3:6==+'''Svar 4.3:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 571: Rad 1 571:
</div> </div>
-==Svar 4.3:7==+'''Svar 4.3:7'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 585: Rad 1 585:
</div> </div>
-==Svar 4.3:8==+'''Svar 4.3:8'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 595: Rad 1 595:
</div> </div>
-==Svar 4.3:9==+'''Svar 4.3:9'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 605: Rad 1 605:
</div> </div>
-==Svar 4.4:1==+'''Svar 4.4:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 633: Rad 1 633:
</div> </div>
-==Svar 4.4:2==+'''Svar 4.4:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 676: Rad 1 676:
</div> </div>
-==Svar 4.4:3==+'''Svar 4.4:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 714: Rad 1 714:
</div> </div>
-==Svar 4.4:4==+'''Svar 4.4:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%" cellpadding="10px"> <table width="100%" cellpadding="10px">
<tr> <tr>
Rad 1 725: Rad 1 725:
</div> </div>
-==Svar 4.4:5==+'''Svar 4.4:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 738: Rad 1 738:
<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td> <td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$x=\displaystyle \frac{n\pi}{3}$</td> <td class="ntext" width="50%">$x=\displaystyle \frac{n\pi}{3}$</td>
-</tr> 
-<tr align="left"> 
<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td> <td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%"> <td class="ntext" width="50%">
Rad 1 751: Rad 1 749:
</div> </div>
-==Svar 4.4:6==+'''Svar 4.4:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 766: Rad 1 764:
x&=\displaystyle \frac{3\pi}{4}+2n\pi}\right.$ x&=\displaystyle \frac{3\pi}{4}+2n\pi}\right.$
</td> </td>
-</tr> 
-<tr align="left"> 
<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td> <td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%"> <td class="ntext" width="50%">
Rad 1 779: Rad 1 775:
</div> </div>
-==Svar 4.4:7==+'''Svar 4.4:7'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 793: Rad 1 789:
<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td> <td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$x=\pm \displaystyle \frac{\pi}{3} + 2n\pi $</td> <td class="ntext" width="50%">$x=\pm \displaystyle \frac{\pi}{3} + 2n\pi $</td>
-</tr> 
-<tr align="left"> 
<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td> <td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%"> <td class="ntext" width="50%">
Rad 1 806: Rad 1 800:
</div> </div>
-==Svar 4.4:8==+'''Svar 4.4:8'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
Rad 1 820: Rad 1 814:
<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td> <td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$x=\displaystyle \frac{\pi}{3}+n\pi$</td> <td class="ntext" width="50%">$x=\displaystyle \frac{\pi}{3}+n\pi$</td>
-</tr> 
-<tr align="left"> 
<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td> <td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%"> <td class="ntext" width="50%">
Rad 1 832: Rad 1 824:
</table> </table>
</div> </div>
 +
 +<br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br>
 +<br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br>
 +<br><br><br><br><br><br><br><br><br>

Nuvarande version

Svar 1.1:1

a)    $-7$ b)    $1$
c)    $11$ d)    $1$

Svar 1.1:2

a)    $0$ b)    $-1$
c)    $-25$ d)    $-19$

Svar 1.1:3

a)    naturliga talen, heltalen, rationella talen b)    heltalen, rationella talen c)    naturliga talen, heltalen, rationella talen
d)    heltalen, rationella talen e)    heltalen, rationella talen f)    naturliga talen, heltalen, rationella talen
g)    rationella talen h)    naturliga talen, heltalen, rationella talen i)    irrationella talen
j)    naturliga talen, heltalen, rationella talen k)    irrationella talen l) irrationella talen

Svar 1.1:4

a)    $\displaystyle \frac{3}{5}<\frac{5}{3}<2<\frac{7}{3}$
b)    $\displaystyle -\frac{1}{2}<-\frac{1}{3}<-\frac{3}{10}<-\frac{1}{5}$
c)    $\displaystyle \frac{1}{2}<\frac{3}{5}<\frac{21}{34}<\frac{5}{8}<\frac{2}{3}$

Svar 1.1:5

a)    $1{,}167$ b)    $2{,}250$ c)    $0{,}286$ d)    $1{,}414$

Svar 1.1:6

a)    Talet är rationellt och lika med $\,314/100 = 157/50\,$.
b)    Talet är rationellt och är lika med $\,31413/9999 = 10471/3333\,$.
c)    Talet är rationellt och lika med $\,1999/9990\,$.
d)    Talet är irrationellt.

Svar 1.2:1

a)    $\displaystyle \frac{93}{28}$ b)    $\displaystyle \frac{3}{35}$ c)    $\displaystyle -\frac{7}{30}$
d)    $\displaystyle \frac{47}{60}$ e)    $\displaystyle \frac{47}{84}$

Svar 1.2:2

a)    $\displaystyle {30}$ b)    $\displaystyle {8}$
c)    $\displaystyle {84}$ d)    $\displaystyle {225}$

Svar 1.2:3

a)    $\displaystyle \frac{19}{100}$ b)    $\displaystyle \frac{1}{240}$

Svar 1.2:4

a)    $\displaystyle \frac{6}{7}$ b)    $\displaystyle \frac{16}{21}$ c)    $\displaystyle \frac{1}{6}$

Svar 1.2:5

a)    $\displaystyle \frac{105}{4}$ b)    $-5$ c)    $\displaystyle \frac{8}{55}$

Svar 1.2:6

$\displaystyle \frac{152}{35}$

Svar 1.3:1

a)    $72$ b)    $3$ c)    $-125$ d)    $\displaystyle \frac{27}{8}$

Svar 1.3:2

a)    $2^6$ b)    $2^{-2}$ c)    $2^0$

Svar 1.3:3

a)    $3^{-1}$ b)    $3^5$ c)    $3^4$ d)    $3^{-3}$ e)    $3^{-3}$

Svar 1.3:4

a)    $4$ b)    $3$ c)    $625$
d)    $16$ e)    $\displaystyle \frac{1}{3750}$

Svar 1.3:5

a)    $2$ b)    $\displaystyle \frac{1}{2}$ c)    $27$
d)    $2209$ e)    $9$ f)    $\displaystyle \frac{25}{3}$

Svar 1.3:6

a)    $256^{1/3}>200^{1/3}$ b)    $0{,}4^{-3}>0{,}5^{-3}$ c)    $0{,}2^{5}>0{,}2^{7}$
d)    $\bigl(5^{1/3}\bigr)^{4}>400^{1/3}$ e)    $125^{1/2}>625^{1/3}$ f)    $3^{40}>2^{56}$

Svar 2.1:1

a)    $3x^2-3x$ b)    $xy+x^2y-x^3y$ c)    $-4x^2+x^2y^2$
d)    $x^3y-x^2y+x^3y^2$ e)    $x^2-14x+49$ f)    $16y^2+40y+25$
g)    $9x^6-6x^3y^2+y^4$ h)    $9x^{10}+30x^8+25x^6$

Svar 2.1:2

a)    $-5x^2+20$ b)    $10x-11$
c)    $54x$ d)    $81x^8-16$
e)    $2a^2+2b^2$

Svar 2.1:3

a)    $(x+6)(x-6)$ b)    $5(x+2)(x-2)$ c)    $(x+3)^2$
d)    $(x-5)^2$ e)    $-2x(x+3)(x-3)$ f)    $(4x+1)^2$

Svar 2.1:4

a)    $5\,$ framför $\,x^2\,$, $\,3\,$ framför $\,x$
b)    $2\,$ framför $\,x^2\,$, $\,1\,$ framför $\,x$
$\textrm{c)    }$ $6\,$ framför $\,x^2\,$, $\,2\,$ framför $\,x$

Svar 2.1:5

a)    $\displaystyle \frac{1}{1-x}$ b)    $-\displaystyle \frac{1}{y(y+2)}$
c)    $3(x-2)(x-1)$ d)    $\displaystyle \frac{2(y+2)}{y^2+4}$

Svar 2.1:6

a)    $2y$ b)    $\displaystyle\frac{-x+12}{(x-2)(x+3)}$
c)    $\displaystyle\frac{b}{a(a-b)   }$ d)    $\displaystyle\frac{a(a+b)   }{4b}$

Svar 2.1:7

a)    $\displaystyle \frac{4}{(x+3)(x+5)}$ b)    $\displaystyle \frac{x^4-x^3+x^2+x-1}{x^2(x-1)}$ c)    $\displaystyle \frac{ax(a+1-x)}{(a+1)^2}$

Svar 2.1:8

a)    $\displaystyle \frac{x}{(x+3)(x+1)}$ b)    $\displaystyle \frac{2(x-3)}{x}$ c)    $\displaystyle \frac{x+2}{2x+3}$

Svar 2.2:1

a)    $x=1$ b)    $x=6$
c)    $x=-\displaystyle\frac{3}{2}$ d)    $x=-\displaystyle\frac{13}{3}$

Svar 2.2:2

a)    $x=1$ b)    $x=\displaystyle\frac{5}{3}$
c)    $x=2$ d)    $x=-2$

Svar 2.2:3

a)    $x=9$
b)    $x=\displaystyle\frac{7}{5}$
c)    $x=\displaystyle\frac{4}{5}$
d)    $x=\displaystyle\frac{1}{2}$

Svar 2.2:4

a)    $-2x+y=3$
b)    $y=-\displaystyle\frac{3}{4}x+\frac{5}{4}$

Svar 2.2:5

a)    $y=-3x+9$
b)    $y=-3x+1$
c)    $y=3x+5$
d)    $y=-\displaystyle \frac{1}{2}x+5$
e)    $k = \displaystyle\frac{8}{5}$

Svar 2.2:6

a)    $\bigl(-\frac{5}{3},0\bigr)$ b)    $(0,5)$
c)    $\bigl(0,-\frac{6}{5}\bigr)$ d)    $(12,-13)$
e)    $\bigl(-\frac{1}{4},\frac{3}{2}\bigr)$

Svar 2.2:7

a)    Bild:Svar_o2_2_7a.gif‎ b)    Bild:Svar_o2_2_7b.gif‎
c)    Bild:Svar_o2_2_7c.gif‎

Svar 2.2:8

a)    Bild:Svar_o2_2_8a.gif‎ b)    Bild:Svar_o2_2_8b.gif‎
c)    Bild:Svar_o2_2_8c.gif‎

Svar 2.2:9

a)    $4\,$ a.e.
b)    $5\,$ a.e.
c)    $6\,$ a.e.


Svar 2.3:1

a)    $(x-1)^2-1$ b)    $(x+1)^2-2$ c)    $-(x-1)^2+6$ d)    $\bigl(x+\frac{5}{2}\bigr)^2-\frac{13}{4}$

Svar 2.3:2

a)    $\left\{ \eqalign{ x_1 &= 1 \cr x_2 &= 3\cr }\right.$ b)    $\left\{ \eqalign{ y_1 &= -5 \cr y_2 &= 3\cr }\right.$ c)    saknar (reella)    lösning
d)    $ \left\{ \eqalign{ x_1 &= \textstyle\frac{1}{2}\cr x_2 &= \textstyle\frac{13}{2}\cr }\right.$ e)    $\left\{ \eqalign{ x_1 &= -1 \cr x_2 &= \textstyle\frac{3}{5}\cr }\right.$ f)    $ \left\{ \eqalign{ x_1 &= \textstyle\frac{4}{3}\cr x_2 &= 2\cr }\right.$

Svar 2.3:3

a)    $\left\{ \eqalign{ x_1 &= 0 \cr x_2 & = -3\cr }\right.$ b)    $\left\{ \eqalign{ x_1 &= 3 \cr x_2 & = -5\cr }\right. $
c)    $\left\{ \eqalign{ x_1 & = \textstyle\frac{2}{3} \cr x_2 & = -8\cr }\right. $ d)    $\left\{ \eqalign{ x_1 & = 0\cr x_2 & = 12\cr }\right. $
e)    $\left\{ \eqalign{ x_1 & = -3 \cr x_2 & = 8\cr }\right. $ f)    $\left\{ \eqalign{ x_1 & = 0 \cr x_2 & = 1 \cr x_3 & = 2 }\right. $

Svar 2.3:4

a)    $ax^2-ax-2a=0\,$, där $\,a\ne 0\,$ är en konstant.
b)    $ax^2-2ax-2a=0\,$, där $\,a\ne 0\,$ är en konstant.
c)    $ax^2-(3+\sqrt{3}\,)ax+3\sqrt{3}\,a=0\,$, där $\,a\ne 0\,$ är en konstant.

Svar 2.3:5

a)    Exempelvis $\ x^2+14x+49=0\,$.
b)    $3< x<4$
c)    $b=-5$

Svar 2.3:6

a)    $0$ b)    $-2$ c)    $\displaystyle \frac{3}{4}$

Svar 2.3:7

a)    $1$ b)    $\displaystyle -\frac{7}{4}$ c)    saknar max

Svar 2.3:8

Se lösningen i webmaterialet när du loggat in till kursen.

Svar 2.3:9

a)    $(-1,0)\ $ och $\ (1,0)$ b)    $(2,0)\ $ och $\ (3,0)$ c)    $(1,0)\ $ och $\ (3,0)$

Svar 2.3:10

Se lösningen i webmaterialet när du loggat in till kursen

Svar 3.1:1

a)    $2^{1/2}$ b)    $7^{5/2}$ c)    $3^{4/3}$ d)    $3^{1/4}$

Svar 3.1:2

a)    $3$ b)    $3$ c)    ej definierad d)    $5^{11/6}$
e)    $12$ f)    $2$ g)    $-5$

Svar 3.1:3

a)    $3$ b)    $\displaystyle \frac{4\sqrt{3}}{3}$
c)    $2\sqrt{5}$ d)    $2-\sqrt{2}$

Svar 3.1:4

a)    $0{,}4$ b)    $0{,}3$
c)    $-4\sqrt{2}$ d)    $2\sqrt{3}$

Svar 3.1:5

a)    $\displaystyle \frac{\sqrt{3}}{3}$ b)    $\displaystyle \frac{7^{2/3}}{7}$ c)    $3-\sqrt{7}$ d)    $\displaystyle \frac{\sqrt{17}+\sqrt{13}}{4}$

Svar 3.1:6

a)    $6+2\sqrt{2}+3\sqrt{5}+\sqrt{10}$ b)    $-\displaystyle \frac{5+4\sqrt{3}}{23}$
c)    $\displaystyle \frac{2}{3}\sqrt{6}+\displaystyle \frac{2}{3}\sqrt{3}-\displaystyle \frac{2}{5}\sqrt{10}-\displaystyle \frac{2}{5}\sqrt{5}$ d)    $\displaystyle \frac{5\sqrt{3}+7\sqrt{2}-\sqrt{6}-12}{23}$

Svar 3.1:7

a)    $\sqrt{5}-\sqrt{7}$ b)    $-\sqrt{35}$ c)    $\sqrt{17}$

Svar 3.1:8

a)    $\sqrt[\scriptstyle3]6 > \sqrt[\scriptstyle3]5$ b)    $7 > \sqrt7$
c)    $\sqrt7 > 2{,}5$ d)    $\sqrt[\scriptstyle3]2\cdot3 > \sqrt2\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3$

Svar 3.2:1

$x=5$

Svar 3.2:2

$x=1$

Svar 3.2:3

$\left \{ \eqalign{ x_1 & = 3 \cr x_2 & = 4\cr } \right.$

Svar 3.2:4

Saknar lösning.

Svar 3.2:5

$x=1$

Svar 3.2:6

$x=\displaystyle\frac{5}{4}$

Svar 3.3:1

a)    $x=3$ b)    $x=-1$
c)    $x=-2$ d)    $x=4$

Svar 3.3:2

a)    $-1$ b)    $4$ c)    $-3$ d)    $0$
e)    $2$ f)    $3$ g)    $10$ h)    $-2$

Svar 3.3:3

a)    $3$ b)    $-\displaystyle \frac{1}{2}$ c)    $-3$
d)    $\displaystyle \frac{7}{3}$ e)    $4$ f)    $-2$
g)    $1$ h)    $\displaystyle \frac{5}{2}$

Svar 3.3:4

a)    $1$ b)    $0$ c)    $-\displaystyle \frac{1}{2}\lg{3}$

Svar 3.3:5

a)    $5$ b)    $0$ c)    $0$
d)    $0$ e)    $-2$ f)    $e^2$

Svar 3.3:6

a)    $1{,}262$
b)    $1{,}663$
c)    $4{,}762$

Svar 3.4:1

a)    $x=\ln 13$ b)    $x=\displaystyle\frac{\ln 2 - \ln 13}{1+\ln 3}$ c)    $x=\displaystyle\frac{\ln 7 - \ln 3}{1-\ln 2}$

Svar 3.4:2

a)    $ \left\{ \eqalign{ x_1&=\sqrt2 \cr x_2&=-\sqrt2 } \right. $ b)    $x=\ln \left(\displaystyle\frac{\sqrt17}{2}-\frac{1}{2}\right)$ c)    Saknar lösning

Svar 3.4:3

a)    $x=-\,\displaystyle\frac{1}{\ln{2}}\pm\sqrt{\left(\displaystyle\frac{1}{\ln{2}}\right)^2-1}$ b)    $x=\displaystyle \frac{5}{2}$
c)    $x=1$

Svar 4.1:1

a)    $90^\circ\ $ och $\ \displaystyle \frac{\pi}{2} \textrm{ rad} $ b)    $135^\circ\ $ och $\ \displaystyle \frac{3\pi}{4} \textrm{ rad}$
c)    $-240^\circ\ $ och $\ \displaystyle -\frac{4\pi}{3} \textrm{ rad}$ d)    $2910^\circ\ $ och $\ \displaystyle \frac{97\pi}{6} \textrm{ rad}$

Svar 4.1:2

a)    $\displaystyle \frac{\pi}{4}\textrm{ rad}$ b)    $\displaystyle \frac{3\pi}{4}\textrm{ rad}$ c)    $-\displaystyle \frac{7\pi}{20}\textrm{ rad}$ d)    $\displaystyle \frac{3\pi}{2}\textrm{ rad}$

Svar 4.1:3

a)    $x=50$ b)    $x=5$ c)    $x=15$

Svar 4.1:4

a)    $5 \textrm{ l.e.}$
b)    $\sqrt{61} \textrm{ l.e.}$
c)    $(2,0)$

Svar 4.1:5

a)    $(x-1)^2+(y-2)^2=4$
b)    $(x-2)^2+(y+1)^2=13$

Svar 4.1:6

a)    En cirkel med radie 3 och medelpunkt i origo. b)    En cirkel med radie $\sqrt 3$ och medelpunkt i punkten (1, 2).
c)    En cirkel med radie $\frac{1}{3}\sqrt 10$ och medelpunkt i punkten (1/3, -7/3).

Svar 4.1:7

a)    En cirkel med medelpunkt (-1, 1) och radie $\sqrt 3$. b)    En cirkel med medelpunkt (0, -2) och radie 2.
c)    En cirkel med medelpunkt (1, -3) och radie $\sqrt 7$.
d)    Endast punkten (1, -1).

Svar 4.1:8

$\displaystyle \frac{10}{\pi}\textrm{ varv }\approx 3,2 \textrm{ varv} $

Svar 4.1:9

$\displaystyle \frac{32\pi}{3} \textrm{ cm}^2 \approx 33,5 \textrm{ cm}^2$

Svar 4.1:10

$x=9$ dm

Svar 4.2:1

Facit till alla delfrågor

a)    $x=13\cdot\tan {27 ^\circ} \approx 6{,}62$ b)    $x=25\cdot\cos {32 ^\circ} \approx 21{,}2$
c)    $x=\displaystyle\frac{14}{\tan {40 ^\circ}} \approx 16{,}7$ d)    $x=\displaystyle\frac{16}{\cos {20 ^\circ}} \approx 17{,}0$
e)    $x=\displaystyle\frac{11}{\sin {35 ^\circ}} \approx 19{,}2$ f)    $x=\displaystyle\frac{19}{\tan {50 ^\circ}} \approx 15{,}9$

Svar 4.2:2

a)    $\tan v=\displaystyle\frac{2}{5}$ b)    $\sin v=\displaystyle\frac{7}{11}$
c)    $\cos v=\displaystyle\frac{5}{7}$ d)    $\sin v=\displaystyle\frac{3}{5}$
e)    $v=30 ^\circ$ f)    $\sin \displaystyle\frac{v}{2}=\displaystyle\frac{1}{3}$

Svar 4.2:3

a)    $-1$ b)    $1$ c)    $0$
d)    $0$ e)    $\displaystyle \frac{1}{\sqrt{2}}$ f)    $\displaystyle \frac{\sqrt{3}}{2}$

Svar 4.2:4

a)    $\displaystyle \frac{\sqrt{3}}{2}$ b)    $\displaystyle \frac{1}{2}$ c)    $-1$
d)    $0$ e)    $\displaystyle \frac{1}{\sqrt{3}}$ f)    $\sqrt{3}$

Svar 4.2:5

a)    $-\displaystyle \frac{1}{\sqrt{2}}$ b)    $1$ c)    $\displaystyle \frac{\sqrt{3}}{2}$ d)    $-1$

Svar 4.2:6

$x= \sqrt{3}-1$

Svar 4.2:7

Älvens bredd är $\ \displaystyle\frac{100}{\sqrt{3}-1}$ m $\approx 136{,}6$ m.


Svar 4.2:8

$\ell\cos \gamma=a \cos \alpha - b\cos \beta $

Svar 4.2:9

Avståndet är $\ \sqrt{205-48\sqrt{3}} \approx 11{,}0$ km.

Svar 4.3:1

a)    $v = \displaystyle \frac{9\pi}{5}$ b)    $v = \displaystyle \frac{6\pi}{7}$ c)    $v = \displaystyle \frac{9\pi}{7}$

Svar 4.3:2

a)    $v=\displaystyle \frac{\pi}{2}$ b)    $v=\displaystyle \frac{3\pi}{5}$

Svar 4.3:3

a)    $-a$ b)    $a$
c)    $\sqrt{1-a^2}$ d)    $\sqrt{1-a^2}$
e)    $-a$ f)    $\displaystyle \frac{\sqrt{3}}{2}\sqrt{1-a^2}+\displaystyle \frac{1}{2}\cdot a $

Svar 4.3:4

a)    $1-b^2$ b)    $\sqrt{1-b^2}$
c)    $2b\sqrt{1-b^2}$ d)    $2b^2-1$
e)    $\sqrt{1-b^2}\cdot\displaystyle \frac{1}{\sqrt{2}} + b\cdot \displaystyle \frac{1}{\sqrt{2}} $ f)    $b\cdot\displaystyle \frac{1}{2}+\sqrt{1-b^2}\cdot\displaystyle \frac{\sqrt{3}}{2}$

Svar 4.3:5

$\cos{v}=\displaystyle \frac{2\sqrt{6}}{7}\quad$ och $\quad\tan{v}=\displaystyle \frac{5}{2\sqrt{6}}\,$.

Svar 4.3:6

a)    $\sin{v}=-\displaystyle \frac{\sqrt{7}}{4}\quad$ och $\quad\tan{v}=-\displaystyle \frac{\sqrt{7}}{3}\,$.
b)    $\cos{v}=-\displaystyle \frac{\sqrt{91}}{10}\quad$ och $\quad\tan{v}=-\displaystyle \frac{3}{\sqrt{91}}\,$.
c)    $\sin{v}=-\displaystyle \frac{3}{\sqrt{10}}\quad$ och $\quad\cos{v}=-\displaystyle \frac{1}{\sqrt{10}}\,$.

Svar 4.3:7

a)    $\sin{(x+y)}=\displaystyle \frac{4\sqrt{2}+\sqrt{5}}{9}$
b)    $\sin{(x+y)}=\displaystyle \frac{3\sqrt{21}+8}{25}$

Svar 4.3:8

Se lösningen i webmaterialet när du loggat in till kursen

Svar 4.3:9

Se lösningen i webmaterialet när du loggat in till kursen

Svar 4.4:1

a)    $\displaystyle v=\frac{\pi}{6}\,$, $\,\displaystyle v=\frac{5\pi}{6}$ b)    $\displaystyle v=\frac{\pi}{3}\,$, $\,\displaystyle v=\frac{5\pi}{3}$
c)    $\displaystyle v=\frac{\pi}{2}$ d)    $\displaystyle v=\frac{\pi}{4}\,$, $\,\displaystyle v=\frac{5\pi}{4}$
e)    lösning saknas f)    $\displaystyle v=\frac{11\pi}{6}\,$, $\,\displaystyle v=\frac{7\pi}{6}$
g)    $\displaystyle v=\frac{5\pi}{6}\,$, $\,\displaystyle v=\frac{11\pi}{6}$

Svar 4.4:2

a)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{3}+2n\pi\cr x&=\displaystyle\frac{2\pi}{3}+2n\pi } \right.$

b)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{3}+2n\pi\cr x&=\displaystyle\frac{5\pi}{3}+2n\pi } \right.$

c)    $x=n\pi$
d)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{20}+\displaystyle\frac{2n\pi}{5}\cr x&=\displaystyle\frac{3\pi}{20}+\displaystyle\frac{2n\pi}{5} } \right.$

e)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{30}+\displaystyle\frac{2n\pi}{5}\cr x&=\displaystyle\frac{\pi}{6}+\displaystyle\frac{2n\pi}{5}} \right.$

f)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{4}+\displaystyle\frac{2n\pi}{3}\cr x&=\displaystyle\frac{5\pi}{12}+\displaystyle\frac{2n\pi}{3}} \right.$

Svar 4.4:3

a)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{6}+2n\pi\cr x&=\displaystyle\frac{11\pi}{6}+2n\pi }\right.$

b)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{5}+2n\pi\cr x&=\displaystyle\frac{4\pi}{5}+2n\pi }\right.$

c)   

$\left\{\eqalign{ x&=25^\circ + n\cdot 360^\circ\cr x&=75^\circ + n\cdot 360^\circ }\right.$

d)   

$\left\{\eqalign{ x&=5^\circ + n \cdot 120^\circ \cr x&= 55^\circ + n \cdot 120^\circ }\right.$

Svar 4.4:4

$v_1=50^\circ$, $\ \ v_2=120^\circ$, $\ \ v_3=230^\circ\ \ $ och $\ \ v_4=300^\circ$

Svar 4.4:5

a)   

$\left\{\eqalign{ x&=n\pi\cr x&=\displaystyle \frac{\pi}{4}+\displaystyle \frac{n\pi}{2} }\right.$

b)    $x=\displaystyle \frac{n\pi}{3}$ c)   

$\left\{\eqalign{ x&=\displaystyle \frac{\pi}{20}+\displaystyle \frac{n\pi}{2}\cr x&=-\displaystyle \frac{\pi}{30}+\displaystyle \frac{n\pi}{3} }\right.$

Svar 4.4:6

a)   

$x=n\pi$

b)   

$\left\{\eqalign{ x&=\displaystyle \frac{\pi}{4}+2n\pi\cr x&=\displaystyle \frac{\pi}{2}+n\pi\cr x&=\displaystyle \frac{3\pi}{4}+2n\pi}\right.$

c)   

$\left\{\eqalign{ x&=\displaystyle \frac{2n\pi}{3}\cr x&=\displaystyle \pi + 2n\pi\cr }\right.$

Svar 4.4:7

a)   

$\left\{ \matrix{ x=\displaystyle \frac{\pi}{6}+2n\pi\cr x=\displaystyle \frac{5\pi}{6}+2n\pi\cr x=\displaystyle \frac{3\pi}{2}+2n\pi }\right.$

b)    $x=\pm \displaystyle \frac{\pi}{3} + 2n\pi $ c)   

$\left\{ \matrix{ x=\displaystyle \frac{\pi}{2}+2n\pi\cr x=\displaystyle \frac{\pi}{14}+\displaystyle \frac{2n\pi}{7} }\right.$

Svar 4.4:8

a)   

$\left\{\eqalign{ x&=\displaystyle \frac{\pi}{4}+2n\pi\cr x&=\displaystyle \frac{\pi}{2}+n\pi\cr x&=\displaystyle \frac{3\pi}{4}+2n\pi }\right.$

b)    $x=\displaystyle \frac{\pi}{3}+n\pi$ c)   

$\left\{\eqalign{ x&=n\pi\cr x&=\displaystyle \frac{3\pi}{4}+n\pi }\right.$












































































Den här artikeln är hämtad från http://wiki.math.se/wikis/sf0600_0701/index.php/Facit
Personliga verktyg