Övn 2.3

Sommarmatte 1

Versionen från 16 juli 2007 kl. 07.57 (redigera) KTH.SE:u1zpa8nw (Diskussion | bidrag) ← Gå till föregående ändring		Nuvarande version (16 juli 2007 kl. 07.59) (redigera) (ogör) KTH.SE:u1zpa8nw (Diskussion | bidrag) (Tar bort sidans innehåll)
(En mellanliggande version visas inte.)
Rad 1:		Rad 1:
-	__NOTOC__
-	==Övning 2.3:1==
-	<div class="ovning">
-	Kvadratkomplettera f&ouml;ljande uttryck
-	<table width="100%" cellspacing="10px">
-	<tr align="left">
-	<td class="ntext">a)</td>
-	<td class="ntext" width="25%">x^2-2x</td>
-	<td class="ntext">b)</td>
-	<td class="ntext" width="25%">x^2+2x-1</td>
-	<td class="ntext">c)</td>
-	<td class="ntext" width="25%">5+2x-x^2</td>
-	<td class="ntext">d)</td>
-	<td class="ntext" width="25%">x^2+5x+3</td>
-	</tr>
-	<tr><td height="5px"/></tr>
-	</table>
-	</div>
-
-	==&Ouml;vning 2.3:2==
-	<div class="ovning">
-	L&ouml;s f&ouml;ljande andragradsekvationer med kvadratkomplettering
-	<table width="100%" cellspacing="10px">
-	<tr align="left">
-	<td class="ntext">a)</td>
-	<td class="ntext" width="33%">x^2-4x+3=0</td>
-	<td class="ntext">b)</td>
-	<td class="ntext" width="33%">y^2+2y-15=0</td>
-	<td class="ntext">c)</td>
-	<td class="ntext" width="33%">y^2+3y+4=0</td>
-	</tr>
-	<tr align="left">
-	<td class="ntext">d)</td>
-	<td class="ntext" width="33%">4x^2-28x+13=0</td>
-	<td class="ntext">e)</td>
-	<td class="ntext" width="33%">5x^2+2x-3=0</td>
-	<td class="ntext">f)</td>
-	<td class="ntext" width="33%">3x^2-10x+8=0</td>
-	</tr>
-	<tr><td height="5px"/></tr>
-	</table>
-	</div>
-
-	==&Ouml;vning 2.3:3==
-	<div class="ovning">
-	L&ouml;s f&ouml;ljande ekvationer direkt
-	<table width="100%" cellspacing="10px">
-	<tr align="left">
-	<td class="ntext">a)</td>
-	<td class="ntext" width="50%">x(x+3)=0</td>
-	<td class="ntext">b)</td>
-	<td class="ntext" width="50%">(x-3)(x+5)=0</td>
-	</tr>
-	<tr align="left">
-	<td class="ntext">c)</td>
-	<td class="ntext" width="50%">5(3x-2)(x+8)=0</td>
-	<td class="ntext">d)</td>
-	<td class="ntext" width="50%">x(x+3)-x(2x-9)=0</td>
-	</tr>
-	<tr align="left">
-	<td class="ntext">e)</td>
-	<td class="ntext" width="50%">(x+3)(x-1)-(x+3)(2x-9)=0</td>
-	<td class="ntext">f)</td>
-	<td class="ntext" width="50%">x(x^2-2x)+x(2-x)=0</td>
-	</tr>
-	<tr><td height="5px"/></tr>
-	</table>
-	</div>
-
-	==&Ouml;vning 2.3:4==
-	<div class="ovning">
-	Best&auml;m en andragradsekvation som har r&ouml;tterna
-	<table width="100%" cellspacing="10px">
-	<tr align="left">
-	<td class="ntext">a)</td>
-	<td class="ntext" width="100%">-1\ och \ 2</td>
-	</tr>
-	<tr align="left">
-	<td class="ntext">b)</td>
-	<td class="ntext" width="100%">1+\sqrt{3}\ och \ 1-\sqrt{3}</td>
-	</tr>
-	<tr align="left">
-	<td class="ntext">c)</td>
-	<td class="ntext" width="100%">3\ och \ \sqrt{3}</td>
-	</tr>
-	<tr><td height="5px"/></tr>
-	</table>
-	</div>
-
-	==&Ouml;vning 2.3:5==
-	<div class="ovning">
-	<table width="100%" cellspacing="10px">
-	<tr align="left">
-	<td class="ntext">a)</td>
-	<td class="ntext" width="100%">Best&auml;m en andragradsekvation som bara har \,-7\, som rot.</td>
-	</tr>
-	<tr>
-	<td class="ntext">b)</td>
-	<td class="ntext" width="100%">Best&auml;m ett v&auml;rde p&aring; \,x\, som g&ouml;r att uttrycket \,4x^2-28x+48\, &auml;r negativt.</td>
-	</tr>
-	<tr>
-	<td class="ntext">c)</td>
-	<td class="ntext" width="100%">Ekvationen \,x^2+4x+b=0\, har en rot \,x=1\,. Best&auml;m v&auml;rdet p&aring; konstanten \,b\,.</td>
-	</tr>
-	<tr><td height="5px"/></tr>
-	</table>
-	</div>
-
-	==&Ouml;vning 2.3:6==
-	<div class="ovning">
-	Best&auml;m det minsta v&auml;rde som f&ouml;ljande polynom antar
-	<table width="100%" cellspacing="10px">
-	<tr align="left">
-	<td class="ntext">a)</td>
-	<td class="ntext" width="33%">x^2-2x+1</td>
-	<td class="ntext">b)</td>
-	<td class="ntext" width="33%">x^2-4x+2</td>
-	<td class="ntext">c)</td>
-	<td class="ntext" width="33%">x^2-5x+7</td>
-	</tr>
-	<tr><td height="5px"/></tr>
-	</table>
-	</div>
-
-	==&Ouml;vning 2.3:7==
-	<div class="ovning">
-	Best&auml;m det st&ouml;rsta v&auml;rde som f&ouml;ljande polynom antar
-	<table width="100%" cellspacing="10px">
-	<tr align="left">
-	<td class="ntext">a)</td>
-	<td class="ntext" width="33%">1-x^2</td>
-	<td class="ntext">b)</td>
-	<td class="ntext" width="33%">-x^2+3x-4</td>
-	<td class="ntext">c)</td>
-	<td class="ntext" width="33%">x^2+x+1</td>
-	</tr>
-	<tr><td height="5px"/></tr>
-	</table>
-	</div>
-
-	==&Ouml;vning 2.3:8==
-	<div class="ovning">
-	Skissera grafen till f&ouml;ljande funktioner
-	<table width="100%" cellspacing="10px">
-	<tr align="left">
-	<td class="ntext">a)</td>
-	<td class="ntext" width="33%">f(x)=x^2+1</td>
-	<td class="ntext">b)</td>
-	<td class="ntext" width="33%">f(x)=(x-1)^2+2</td>
-	<td class="ntext">c)</td>
-	<td class="ntext" width="33%">f(x)=x^2-6x+11</td>
-	</tr>
-	<tr><td height="5px"/></tr>
-	</table>
-	</div>
-
-	==&Ouml;vning 2.3:9==
-	<div class="ovning">
-	Hitta alla sk&auml;rningspunkter mellan x-axeln och kurvan
-	<table width="100%" cellspacing="10px">
-	<tr align="left">
-	<td class="ntext">a)</td>
-	<td class="ntext" width="33%">y=x^2-1</td>
-	<td class="ntext">b)</td>
-	<td class="ntext" width="33%">y=x^2-5x+6</td>
-	<td class="ntext">c)</td>
-	<td class="ntext" width="33%">y=3x^2-12x+9</td>
-	</tr>
-	<tr><td height="5px"/></tr>
-	</table>
-	</div>
-
-	==&Ouml;vning 2.3:10==
-	<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="50%">y \geq x^2\ och \ y \leq 1 </td>
-	<td class="ntext">b)</td>
-	<td class="ntext" width="50%">y \leq 1-x^2\ och \ x \geq 2y-3 </td>
-	</tr>
-	<tr align="left">
-	<td class="ntext">c)</td>
-	<td class="ntext" width="50%">1 \geq x \geq y^2 </td>
-	<td class="ntext">d)</td>
-	<td class="ntext" width="50%">x^2 \leq y \leq x </td>
-	</tr>
-	<tr><td height="5px"/></tr>
-	</table>
-	</div>

---

Nuvarande version