1.3 Övningar
Sommarmatte 1
(Skillnad mellan versioner)
| Versionen från 28 april 2007 kl. 13.08 (redigera) Ossiang (Diskussion | bidrag) (→Övning 1.3:2) ← Gå till föregående ändring |
Nuvarande version (25 maj 2007 kl. 11.14) (redigera) (ogör) KTH.SE:u1qh5fat (Diskussion | bidrag) (→Övning 1.3:4) |
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| (14 mellanliggande versioner visas inte.) | |||
| Rad 4: | Rad 4: | ||
| Beräkna | Beräkna | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">$\textrm{a) }$</td> | + | <td class="ntext">a)</td> |
| - | <td class="ntext">$2^3\cdot3^2$</td> | + | <td class="ntext" width="25%">$2^3\cdot3^2$</td> |
| - | <td class="ntext">$\textrm{b) }$</td> | + | <td class="ntext">b)</td> |
| - | <td class="ntext">$3^5\cdot9^{-2}$</td> | + | <td class="ntext" width="25%">$3^5\cdot9^{-2}$</td> |
| - | <td class="ntext">$\textrm{c) }$</td> | + | <td class="ntext">c)</td> |
| - | <td class="ntext">$(-5)^3$</td> | + | <td class="ntext" width="25%">$(-5)^3$</td> |
| - | <td class="ntext">$\textrm{d) }$</td> | + | <td class="ntext">d)</td> |
| - | <td class="ntext">$\left(\displaystyle \frac{2}{3}\right)^{-3}$</td> | + | <td class="ntext" width="25%">$\Bigl(\displaystyle \frac{2}{3}\Bigr)^{-3}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 22: | Rad 21: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">$\textrm{a) }$</td> | + | <td class="ntext">a)</td> |
| - | <td class="ntext">$72$</td> | + | <td class="ntext" width="25%">$72$</td> |
| - | <td class="ntext">$\textrm{b) }$</td> | + | <td class="ntext">b)</td> |
| - | <td class="ntext">$3$</td> | + | <td class="ntext" width="25%">$3$</td> |
| - | <td class="ntext">$\textrm{c) }$</td> | + | <td class="ntext">c)</td> |
| - | <td class="ntext">$-125$</td> | + | <td class="ntext" width="25%">$-125$</td> |
| - | <td class="ntext">$\textrm{d) }$</td> | + | <td class="ntext">d)</td> |
| - | <td class="ntext">$\displaystyle \frac{27}{8}$</td> | + | <td class="ntext" width="25%">$\displaystyle \frac{27}{8}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 41: | Rad 39: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:1_3_1a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_1a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:1_3_1b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_1b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:1_3_1c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_1c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning d </div> | + | <div class=NavHead>Lösning d) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga d<br \>[[Bild:1_3_1d.gif]] | + | Lösning till delfråga d) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_1d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 73: | Rad 99: | ||
| Skriv som en potens av 2 | Skriv som en potens av 2 | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| + | <tr align="left"> | ||
| + | <td class="ntext">a)</td> | ||
| + | <td class="ntext" width="33%">$2\cdot4\cdot8$</td> | ||
| + | <td class="ntext">b)</td> | ||
| + | <td class="ntext" width="33%">$0{,}25$</td> | ||
| + | <td class="ntext">c)</td> | ||
| + | <td class="ntext" width="33%">$1$</td> | ||
| + | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Facit </div> | ||
| + | <div class=NavContent> | ||
| + | Facit till alla delfrågor<br \> | ||
| + | <table width="100%" cellspacing="10px"> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">$\textrm{a) }$</td> | + | <td class="ntext">a)</td> |
| - | <td class="ntext"> $2\cdot4\cdot8$</td> | + | <td class="ntext" width="33%">$2^6$</td> |
| - | <td class="ntext">$\textrm{b) }$</td> | + | <td class="ntext">b)</td> |
| - | <td class="ntext">$0,25$</td> | + | <td class="ntext" width="33%">$2^{-2}$</td> |
| - | <td class="ntext">$\textrm{c) }$</td> | + | <td class="ntext">c)</td> |
| - | <td class="ntext">$\textrm{1}$</td> | + | <td class="ntext" width="33%">$2^0$</td> |
| + | </tr> | ||
| + | <tr><td height="5px"/></tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning a) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga a) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_2a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning b) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga b) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_2b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning c) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga c) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_2c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | ==Övning 1.3:3== | ||
| + | |||
| + | <div class="ovning"> | ||
| + | Skriv som en potens av 3 | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr align="left"> | ||
| + | <td class="ntext">a)</td> | ||
| + | <td class="ntext" width="20%">$\displaystyle \frac{1}{3}$</td> | ||
| + | <td class="ntext">b)</td> | ||
| + | <td class="ntext" width="20%">$243$</td> | ||
| + | <td class="ntext">c)</td> | ||
| + | <td class="ntext" width="20%">$9^2$</td> | ||
| + | <td class="ntext">d)</td> | ||
| + | <td class="ntext" width="20%">$\displaystyle \frac{1}{27}$</td> | ||
| + | <td class="ntext">e)</td> | ||
| + | <td class="ntext" width="20%">$\displaystyle \frac{3}{9^2}$</td> | ||
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 89: | Rad 195: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor<br \> |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| + | <tr align="left"> | ||
| + | <td class="ntext">a)</td> | ||
| + | <td class="ntext" width="20%">$3^{-1}$</td> | ||
| + | <td class="ntext">b)</td> | ||
| + | <td class="ntext" width="20%">$3^5$</td> | ||
| + | <td class="ntext">c)</td> | ||
| + | <td class="ntext" width="20%">$3^4$</td> | ||
| + | <td class="ntext">d)</td> | ||
| + | <td class="ntext" width="20%">$3^{-3}$</td> | ||
| + | <td class="ntext">e)</td> | ||
| + | <td class="ntext" width="20%">$3^{-3}$</td> | ||
| + | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning a) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga a) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_3a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning b) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga b) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_3b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning c) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga c) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_3c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning d) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga d) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_3d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning e) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga e) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_3e.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | ==Övning 1.3:4== | ||
| + | |||
| + | <div class="ovning"> | ||
| + | Beräkna | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr align="left"> | ||
| + | <td class="ntext">a)</td> | ||
| + | <td class="ntext" width="33%">$2^{9}\cdot2^{-7}$</td> | ||
| + | <td class="ntext">b)</td> | ||
| + | <td class="ntext" width="33%">$3^{13}\cdot9^{-3}\cdot27^{\,-2}$</td> | ||
| + | <td class="ntext">c)</td> | ||
| + | <td class="ntext" width="33%">$\displaystyle \frac{5^{12}}{5^{-4}}\cdot(5^{2})^{-6}$</td> | ||
| + | </tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">$\textrm{a) }$</td> | + | <td class="ntext">d)</td> |
| - | <td class="ntext"> $2^6$</td> | + | <td class="ntext" width="33%">$2^{2^{\scriptstyle3}}\cdot(-2)^{\scriptstyle-4}$</td> |
| - | <td class="ntext">$\textrm{b) }$</td> | + | <td class="ntext">e)</td> |
| - | <td class="ntext">$2^{-2}$</td> | + | <td class="ntext" width="33%">$625\cdot(5^{8}+5^{9})^{-1}$</td> |
| - | <td class="ntext">$\textrm{c) }$</td> | + | </tr> |
| - | <td class="ntext">$2^0$</td> | + | <tr><td height="5px"/></tr> |
| + | </table> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Facit </div> | ||
| + | <div class=NavContent> | ||
| + | Facit till alla delfrågor | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr align="left"> | ||
| + | <td class="ntext">a)</td> | ||
| + | <td class="ntext" width="33%">$4$</td> | ||
| + | <td class="ntext">b)</td> | ||
| + | <td class="ntext" width="33%">$3$</td> | ||
| + | <td class="ntext">c)</td> | ||
| + | <td class="ntext" width="33%">$625$</td> | ||
| + | </tr> | ||
| + | <tr align="left"> | ||
| + | <td class="ntext">d)</td> | ||
| + | <td class="ntext" width="33%">$16$</td> | ||
| + | <td class="ntext">e)</td> | ||
| + | <td class="ntext" width="33%">$\displaystyle \frac{1}{3750}$</td> | ||
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 106: | Rad 332: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:1_3_2a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_4a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:1_3_2b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_4b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:1_3_2c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_4c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| - | ==Övning 1.3:3== | + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning d) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga d) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_4d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning e) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga e) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_4e.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | ==Övning 1.3:5== | ||
| + | |||
| + | <div class="ovning"> | ||
| + | Beräkna | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr align="left"> | ||
| + | <td class="ntext">a)</td> | ||
| + | <td class="ntext" width="33%">$4^{1/2}$</td> | ||
| + | <td class="ntext">b)</td> | ||
| + | <td class="ntext" width="33%">$4^{-1/2}$</td> | ||
| + | <td class="ntext">c)</td> | ||
| + | <td class="ntext" width="33%">$9^{3/2}$</td> | ||
| + | </tr> | ||
| + | <tr align="left"> | ||
| + | <td class="ntext">d)</td> | ||
| + | <td class="ntext" width="33%">$\left(47^{2/3} \right) ^{3}$</td> | ||
| + | <td class="ntext">e)</td> | ||
| + | <td class="ntext" width="33%">$3^{1{,}4}\cdot3^{0{,}6}$</td> | ||
| + | <td class="ntext">f)</td> | ||
| + | <td class="ntext" width="33%">$\bigl( 125 ^{1/3} \bigr)^2\cdot \bigl( 27^{1/3} \bigr)^{-2}\cdot9^{1/2}$</td> | ||
| + | </tr> | ||
| + | <tr><td height="5px"/></tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Facit </div> | ||
| + | <div class=NavContent> | ||
| + | Facit till alla delfrågor<br \> | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr align="left"> | ||
| + | <td class="ntext">a)</td> | ||
| + | <td class="ntext" width="33%">$2$</td> | ||
| + | <td class="ntext">b)</td> | ||
| + | <td class="ntext" width="33%">$\displaystyle \frac{1}{2}$</td> | ||
| + | <td class="ntext">c)</td> | ||
| + | <td class="ntext" width="33%">$27$</td> | ||
| + | </tr> | ||
| + | <tr align="left"> | ||
| + | <td class="ntext">d)</td> | ||
| + | <td class="ntext" width="33%">$2209$</td> | ||
| + | <td class="ntext">e)</td> | ||
| + | <td class="ntext" width="33%">$9$</td> | ||
| + | <td class="ntext">f)</td> | ||
| + | <td class="ntext" width="33%">$\displaystyle \frac{25}{3}$</td> | ||
| + | </tr> | ||
| + | <tr><td height="5px"/></tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning a) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga a) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_5a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning b) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga b) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_5b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning c) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga c) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_5c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning d) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga d) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_5d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning e) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga e) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_5e.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning f) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga f) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_5f.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | ==Övning 1.3:6== | ||
| + | <div class="ovning"> | ||
| + | Avgör vilket tal som är störst av | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr align="left"> | ||
| + | <td class="ntext">a)</td> | ||
| + | <td class="ntext" width="33%">$256^{1/3}\ $ och $\ 200^{1/3}$</td> | ||
| + | <td class="ntext">b)</td> | ||
| + | <td class="ntext" width="33%">$0{,}5^{-3}\ $ och $\ 0{,}4^{-3}$</td> | ||
| + | <td class="ntext">c)</td> | ||
| + | <td class="ntext" width="33%">$0{,}2^5\ $ och $\ 0{,}2^{7}$</td> | ||
| + | </tr> | ||
| + | <tr align="left"> | ||
| + | <td class="ntext">d)</td> | ||
| + | <td class="ntext" width="33%">$400^{1/3}\ $ och $\ \bigl(5^{1/3}\bigr)^{4}$</td> | ||
| + | <td class="ntext">e)</td> | ||
| + | <td class="ntext" width="33%">$125^{1/2}\ $ och $\ 625^{1/3}$</td> | ||
| + | <td class="ntext">f)</td> | ||
| + | <td class="ntext" width="33%">$2^{56}\ $ och $\ 3^{40}$</td> | ||
| + | </tr> | ||
| + | <tr><td height="5px"/></tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Facit </div> | ||
| + | <div class=NavContent> | ||
| + | Facit till alla delfrågor<br \> | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr align="left"> | ||
| + | <td class="ntext">a)</td> | ||
| + | <td class="ntext" width="33%">$256^{1/3}>200^{1/3}$</td> | ||
| + | <td class="ntext">b)</td> | ||
| + | <td class="ntext" width="33%">$0{,}4^{-3}>0{,}5^{-3}$</td> | ||
| + | <td class="ntext">c)</td> | ||
| + | <td class="ntext" width="33%">$0{,}2^{5}>0{,}2^{7}$</td> | ||
| + | </tr> | ||
| + | <tr align="left"> | ||
| + | <td class="ntext">d)</td> | ||
| + | <td class="ntext" width="33%">$\bigl(5^{1/3}\bigr)^{4}>400^{1/3}$</td> | ||
| + | <td class="ntext">e)</td> | ||
| + | <td class="ntext" width="33%">$125^{1/2}>625^{1/3}$</td> | ||
| + | <td class="ntext">f)</td> | ||
| + | <td class="ntext" width="33%">$3^{40}>2^{56}$</td> | ||
| + | </tr> | ||
| + | <tr><td height="5px"/></tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning a) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga a) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_6a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning b) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga b) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_6b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning c) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga c) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_6c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning d) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga d) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_6d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning e) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga e) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_6e.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
| + | |||
| + | <div class=NavFrame style="CLEAR: both"> | ||
| + | <div class=NavHead>Lösning f) </div> | ||
| + | <div class=NavContent> | ||
| + | Lösning till delfråga f) | ||
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_6f.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | </div> | ||
| + | </div> | ||
Nuvarande version
Innehåll |
[redigera] Övning 1.3:1
Beräkna
| a) | $2^3\cdot3^2$ | b) | $3^5\cdot9^{-2}$ | c) | $(-5)^3$ | d) | $\Bigl(\displaystyle \frac{2}{3}\Bigr)^{-3}$ |
Facit
Facit till alla delfrågor
| a) | $72$ | b) | $3$ | c) | $-125$ | d) | $\displaystyle \frac{27}{8}$ |
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Lösning d)
Lösning till delfråga d)
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[redigera] Övning 1.3:2
Skriv som en potens av 2
| a) | $2\cdot4\cdot8$ | b) | $0{,}25$ | c) | $1$ |
Facit
Facit till alla delfrågor
| a) | $2^6$ | b) | $2^{-2}$ | c) | $2^0$ |
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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[redigera] Övning 1.3:3
Skriv som en potens av 3
| a) | $\displaystyle \frac{1}{3}$ | b) | $243$ | c) | $9^2$ | d) | $\displaystyle \frac{1}{27}$ | e) | $\displaystyle \frac{3}{9^2}$ |
Facit
Facit till alla delfrågor
| a) | $3^{-1}$ | b) | $3^5$ | c) | $3^4$ | d) | $3^{-3}$ | e) | $3^{-3}$ |
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Lösning d)
Lösning till delfråga d)
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Lösning e)
Lösning till delfråga e)
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[redigera] Övning 1.3:4
Beräkna
| a) | $2^{9}\cdot2^{-7}$ | b) | $3^{13}\cdot9^{-3}\cdot27^{\,-2}$ | c) | $\displaystyle \frac{5^{12}}{5^{-4}}\cdot(5^{2})^{-6}$ |
| d) | $2^{2^{\scriptstyle3}}\cdot(-2)^{\scriptstyle-4}$ | e) | $625\cdot(5^{8}+5^{9})^{-1}$ | ||
Facit
Facit till alla delfrågor
| a) | $4$ | b) | $3$ | c) | $625$ |
| d) | $16$ | e) | $\displaystyle \frac{1}{3750}$ | ||
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Lösning d)
Lösning till delfråga d)
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Lösning e)
Lösning till delfråga e)
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[redigera] Övning 1.3:5
Beräkna
| a) | $4^{1/2}$ | b) | $4^{-1/2}$ | c) | $9^{3/2}$ |
| d) | $\left(47^{2/3} \right) ^{3}$ | e) | $3^{1{,}4}\cdot3^{0{,}6}$ | f) | $\bigl( 125 ^{1/3} \bigr)^2\cdot \bigl( 27^{1/3} \bigr)^{-2}\cdot9^{1/2}$ |
Facit
Facit till alla delfrågor
| a) | $2$ | b) | $\displaystyle \frac{1}{2}$ | c) | $27$ |
| d) | $2209$ | e) | $9$ | f) | $\displaystyle \frac{25}{3}$ |
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Lösning d)
Lösning till delfråga d)
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Lösning e)
Lösning till delfråga e)
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Lösning f)
Lösning till delfråga f)
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[redigera] Övning 1.3:6
Avgör vilket tal som är störst av
| a) | $256^{1/3}\ $ och $\ 200^{1/3}$ | b) | $0{,}5^{-3}\ $ och $\ 0{,}4^{-3}$ | c) | $0{,}2^5\ $ och $\ 0{,}2^{7}$ |
| d) | $400^{1/3}\ $ och $\ \bigl(5^{1/3}\bigr)^{4}$ | e) | $125^{1/2}\ $ och $\ 625^{1/3}$ | f) | $2^{56}\ $ och $\ 3^{40}$ |
Facit
Facit till alla delfrågor
| 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) | $3^{40}>2^{56}$ |
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Lösning d)
Lösning till delfråga d)
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Lösning e)
Lösning till delfråga e)
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Lösning f)
Lösning till delfråga f)
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