Övn 2.1

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Versionen från 16 juli 2007 kl. 07.52 (redigera)
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(Ny sida: __NOTOC__ ==Övning 2.1:1== <div class="ovning"> Utveckla <table width="100%" cellspacing="10px"> <tr align="left"> <td class="ntext">a)</td> <td class="ntext" width="33%">$3x(x-1)$</td> <...)
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Rad 1: Rad 1:
-__NOTOC__ 
-==Övning 2.1:1== 
-<div class="ovning"> 
-Utveckla 
-<table width="100%" cellspacing="10px"> 
-<tr align="left"> 
-<td class="ntext">a)</td> 
-<td class="ntext" width="33%">$3x(x-1)$</td> 
-<td class="ntext">b)</td> 
-<td class="ntext" width="33%">$(1+x-x^2)xy$</td> 
-<td class="ntext">c)</td> 
-<td class="ntext" width="33%">$-x^2(4-y^2)$</td> 
-</tr> 
-<tr align="left"> 
-<td class="ntext">d)</td> 
-<td class="ntext" width="33%">$x^3y^2\left(\displaystyle \frac{1}{y} - \frac{1}{xy}+1\right)$</td> 
-<td class="ntext">e) </td> 
-<td class="ntext" width="33%">$(x-7)^2$</td> 
-<td class="ntext">f)</td> 
-<td class="ntext" width="33%">$(5+4y)^2$</td> 
-</tr> 
-<tr align="left"> 
-<td class="ntext">g)</td> 
-<td class="ntext" width="33%">$(y^2-3x^3)^2$</td> 
-<td class="ntext">h)</td> 
-<td class="ntext" width="33%">$(5x^3+3x^5)^2$</td> 
-</tr> 
-<tr><td height="5px"/></tr> 
-</table> 
-</div> 
- 
-==Övning 2.1:2== 
-<div class="ovning"> 
-Utveckla och förenkla så långt som möjligt 
-<table width="100%" cellspacing="10px"> 
-<tr align="left"> 
-<td class="ntext">a)</td> 
-<td class="ntext" width="50%">$(x-4)(x-5)-3x(2x-3)$</td> 
-<td class="ntext">b)</td> 
-<td class="ntext" width="50%">$(1-5x)(1+15x)-3(2-5x)(2+5x)$</td> 
-</tr> 
-<tr align="left"> 
-<td class="ntext">c)</td> 
-<td class="ntext" width="50%">$(3x+4)^2-(3x-2)(3x-8)$</td> 
-<td class="ntext">d)</td> 
-<td class="ntext" width="50%">$(3x^2+2)(3x^2-2)(9x^4+4)$</td> 
-</tr> 
-<tr align="left"> 
-<td class="ntext">e)</td> 
-<td class="ntext" width="50%">$(a+b)^2+(a-b)^2$</td> 
-</tr> 
-<tr><td height="5px"/></tr> 
-</table> 
-</div> 
- 
-==Övning 2.1:3== 
- 
-<div class="ovning"> 
-Faktorisera s&aring; l&aring;ngt som m&ouml;jligt 
-<table width="100%" cellspacing="10px"> 
-<tr align="left"> 
-<td class="ntext">a)</td> 
-<td class="ntext" width="33%">$x^2-36$</td> 
-<td class="ntext">b)</td> 
-<td class="ntext" width="33%">$5x^2-20$</td> 
-<td class="ntext">c)</td> 
-<td class="ntext" width="33%">$x^2+6x+9$</td> 
-</tr> 
-<tr align="left"> 
-<td class="ntext">d)</td> 
-<td class="ntext" width="33%">$x^2-10x+25$</td> 
-<td class="ntext">e)</td> 
-<td class="ntext" width="33%">$18x-2x^3$</td> 
-<td class="ntext">f)</td> 
-<td class="ntext" width="33%">$16x^2+8x+1$</td> 
-</tr> 
-<tr><td height="5px"/></tr> 
-</table> 
-</div> 
- 
-==Övning 2.1:4== 
-<div class="ovning"> 
-Bestäm koefficienterna framför $\,x\,$ och $\,x^2\,$ när följande uttryck utvecklas 
-<table width="100%" cellspacing="10px"> 
-<tr align="left"> 
-<td class="ntext">a)</td> 
-<td class="ntext" width="100%">$(x+2)(3x^2-x+5)$</td> 
-</tr> 
-<tr align="left"> 
-<td class="ntext">b)</td> 
-<td class="ntext" width="100%">$(1+x+x^2+x^3)(2-x+x^2+x^4)$</td> 
-</tr> 
-<tr align="left"> 
-<td class="ntext">c)</td> 
-<td class="ntext" width="100%">$(x-x^3+x^5)(1+3x+5x^2)(2-7x^2-x^4)$</td> 
-</tr> 
-<tr><td height="5px"/></tr> 
-</table> 
-</div> 
- 
-==Övning 2.1:5== 
-<div class="ovning"> 
-Förenkla så långt som möjligt 
-<table width="100%" cellspacing="10px"> 
-<tr align="left"> 
-<td class="ntext">a)</td> 
-<td class="ntext" width="50%">$\displaystyle \frac{1}{x-x^2}-\displaystyle \frac{1}{x}$</td> 
-<td class="ntext">b)</td> 
-<td class="ntext" width="50%">$\displaystyle \frac{1}{y^2-2y}-\displaystyle \frac{2}{y^2-4}$</td> 
-</tr> 
-<tr align="left"> 
-<td class="ntext">c)</td> 
-<td class="ntext" width="50%">$\displaystyle \frac{(3x^2-12)(x^2-1)}{(x+1)(x+2)}$</td> 
-<td class="ntext">d)</td> 
-<td class="ntext" width="50%">$\displaystyle \frac{(y^2+4y+4)(2y-4)}{(y^2+4)(y^2-4)}$</td> 
-</tr> 
-</table> 
-</div> 
- 
-==Övning 2.1:6== 
-<div class="ovning"> 
-Förenkla så långt som möjligt 
-<table width="100%" cellspacing="10px"> 
-<tr align="left"> 
-<td class="ntext">a)</td> 
-<td class="ntext" width="50%">$\left(x-y+\displaystyle\frac{x^2}{y-x}\right)$ $\left(\displaystyle\frac{y}{2x-y}-1\right)$</td> 
-<td class="ntext">b)</td> 
-<td class="ntext" width="50%">$\displaystyle \frac{x}{x-2}+\displaystyle \frac{x}{x+3}-2$</td> 
-</tr> 
-<tr align="left"> 
-<td class="ntext">c)</td> 
-<td class="ntext" width="50%">$\displaystyle \frac{2a+b}{a^2-ab}-\frac{2}{a-b}$</td> 
-<td class="ntext">d)</td> 
-<td class="ntext" width="50%">$\displaystyle\frac{a-b+\displaystyle\frac{b^2}{a+b}}{1-\left(\displaystyle\frac{a-b}{a+b}\right)^2}$</td> 
-</tr> 
-<tr><td height="5px"/></tr> 
-</table> 
-</div> 
- 
-==Övning 2.1:7== 
-<div class="ovning"> 
-Förenkla följande bråkuttryck genom att skriva på gemensamt bråkstreck 
-<table width="100%" cellspacing="10px"> 
-<tr align="left"> 
-<td class="ntext">a)</td> 
-<td class="ntext" width="33%">$\displaystyle \frac{2}{x+3}-\frac{2}{x+5}$</td> 
-<td class="ntext">b)</td> 
-<td class="ntext" width="33%">$x+\displaystyle \frac{1}{x-1}+\displaystyle \frac{1}{x^2}$</td> 
-<td class="ntext">c)</td> 
-<td class="ntext" width="33%">$\displaystyle \frac{ax}{a+1}-\displaystyle \frac{ax^2}{(a+1)^2}$</td> 
-</tr> 
-</table> 
-</div> 
- 
-==Övning 2.1:8== 
- 
-<div class="ovning"> 
-Förenkla följande bråkuttryck genom att skriva på gemensamt bråkstreck 
-<table width="100%" cellspacing="10px"> 
-<tr> 
-<td class="ntext">a)</td> 
-<td class="ntext" width="33%">$\displaystyle \frac{\displaystyle\ \frac{x}{x+1}\ }{\ 3+x\ }$</td> 
-<td class="ntext">b)</td> 
-<td class="ntext" width="33%">$\displaystyle \frac{\displaystyle \frac{3}{x}-\displaystyle \frac{1}{x}}{\displaystyle \frac{1}{x-3}}$</td> 
-<td class="ntext">c)</td> 
-<td class="ntext" width="33%">$\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+x}}}$</td> 
-</tr> 
-<tr><td height="5px"/></tr> 
-</table> 
-</div> 

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