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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| - | __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> | ||
