Övn 2.2
Sommarmatte 1
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| Versionen från 16 juli 2007 kl. 07.56 (redigera) KTH.SE:u1zpa8nw (Diskussion | bidrag) (Ny sida: __NOTOC__ ==Övning 2.2:1== <div class="ovning"> Lös ekvationerna <table width="100%" cellspacing="10px"> <tr align="left"> <td class="ntext">a)</td> <td class="ntext" width="50%">$x-2...) ← Gå till föregående ändring |
Nuvarande version (16 juli 2007 kl. 08.00) (redigera) (ogör) KTH.SE:u1zpa8nw (Diskussion | bidrag) (Tar bort sidans innehåll) |
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| Rad 1: | Rad 1: | ||
| - | __NOTOC__ | ||
| - | ==Övning 2.2:1== | ||
| - | <div class="ovning"> | ||
| - | Lös ekvationerna | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="50%">$x-2=-1$</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="50%">$2x+1=13$</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="50%">$\displaystyle\frac{1}{3}x-1=x$</td> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="50%">$5x+7=2x-6$</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | ==Övning 2.2:2== | ||
| - | <div class="ovning"> | ||
| - | Lös ekvationerna | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="50%">$\displaystyle\frac{5x}{6}-\displaystyle\frac{x+2}{9}=\displaystyle\frac{1}{2}$</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="50%">$\displaystyle\frac{8x+3}{7}-\displaystyle\frac{5x-7}{4}=2$</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="50%">$(x+3)^2-(x-5)^2=6x+4$</td> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="50%">$(x^2+4x+1)^2+3x^4-2x^2=(2x^2+2x+3)^2$</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 2.2:3== | ||
| - | <div class="ovning"> | ||
| - | Lös ekvationerna | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="100%">$\displaystyle\frac{x+3}{x-3}-\displaystyle\frac{x+5}{x-2}=0$</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="100%">$\displaystyle\frac{4x}{4x-7}-\displaystyle\frac{1}{2x-3}=1$</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="100%">$\left(\displaystyle\frac{1}{x-1}-\frac{1}{x+1}\right)\left(x^2+\frac{1}{2}\right)=\displaystyle\frac{6x-1}{3x-3}$</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">d) </td> | ||
| - | <td class="ntext" width="100%"> $\left(\displaystyle\frac{2}{x}-3\right)\left(\displaystyle\frac{1}{4x}+\frac{1}{2}\right)-\left(\displaystyle\frac{1}{2x}-\frac{2}{3}\right)^2-\left(\displaystyle\frac{1}{2x}+\frac{1}{3}\right)\left(\displaystyle\frac{1}{2x}-\frac{1}{3}\right)=0$</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 2.2:4== | ||
| - | <div class="ovning"> | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td>a)</td> | ||
| - | <td width="100%">Skriv ekvationen för linjen $\,y=2x+3\,$ på formen $\,ax+by=c\,$.</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td>b)</td> | ||
| - | <td width="100%">Skriv ekvationen för linjen $\,3x+4y-5=0\,$ på formen $\,y=kx+m\,$.</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"\></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 2.2:5== | ||
| - | <div class="ovning"> | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left" valign="top"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="100%">Bestäm ekvationen för den räta linje som går genom punkterna $\,(2,3)\,$ och $\,(3,0)\,$.</td> | ||
| - | </tr> | ||
| - | <tr align="left" valign="top"> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="100%">Bestäm ekvationen för den räta linje som har riktningskoefficient $\,-3\,$ och går genom punkten $\,(1,-2)\,$.</td> | ||
| - | </tr> | ||
| - | <tr align="left" valign="top"> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="100%">Bestäm ekvationen för den räta linje som går genom punkten $\,(-1,2)\,$ och är parallell med linjen $\,y=3x+1\,$.</td> | ||
| - | </tr> | ||
| - | <tr align="left" valign="top"> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="100%">Bestäm ekvationen för den räta linje som går genom punkten $\,(2,4)\,$ och är vinkelrät mot linjen $\,y=2x+5\,$.</td> | ||
| - | </tr> | ||
| - | <tr align="left" valign="top"> | ||
| - | <td class="ntext">e)</td> | ||
| - | <td class="ntext" width="100%">Bestäm riktningskoefficienten, $\,k\,$, för den räta linje som skär ''x''-axeln i punkten $\,(5,0)\,$ och ''y''-axeln i punkten $\,(0,-8)\,$.</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 2.2:6== | ||
| - | <div class="ovning"> | ||
| - | Finn skärningspunkten mellan följande linjer | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="50%">$y=3x+5\ $ och ''x''-axeln</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="50%">$y=-x+5\ $ och ''y''-axeln</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="50%">$4x+5y+6=0\ $ och ''y''-axeln</td> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="50%">$x+y+1=0\ $ och $\ x=12$</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">e)</td> | ||
| - | <td class="ntext" width="50%">$2x+y-1=0\ $ och $\ y-2x-2=0$</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 2.2:7== | ||
| - | <div class="ovning"> | ||
| - | Skissera grafen till följande funktioner | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="33%">$f(x)=3x-2$</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="33%">$f(x)=2-x$</td> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="33%">$f(x)=2$</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 2.2:8== | ||
| - | <div class="ovning"> | ||
| - | Rita in i ett ''xy''-plan alla punkter vars koordinater $\,(x,y)\,$ uppfyller | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="33%">$y \geq x $</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="33%">$y < 3x -4 $</td> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="33%">$2x+3y \leq 6 $</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 2.2:9== | ||
| - | <div class="ovning"> | ||
| - | Beräkna arean av den triangel som | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="100%">har hörn i punkterna $\,(1,4)\,$, $\,(3,3)\,$ och $\,(1,0)\,$</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="100%">begränsas av linjerna $\ x=2y\,$, $\ y=4\ $ och $\ y=10-2x\,$</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="100%">beskrivs av olikheterna $\ x+y \geq -2\,$, $\ 2x-y \leq 2\ $ och $\ 2y-x \leq 2\,$</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
