Forskjell mellom versjoner av «1T 2012 høst LØSNING»
| Linje 27: | Linje 27: | ||
<tr> | <tr> | ||
<td> </td> | <td> </td> | ||
| − | <td>''' | + | <td>''' ''Bio'' '''</td> |
| − | <td>''' | + | <td>''' ''<tex>\bar{Bio}</tex>'' '''</td> |
<td>'''Sum '''</td> | <td>'''Sum '''</td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <td>''' | + | <td>''' ''Fys'' '''</td> |
| − | <td> <tex> | + | <td> <tex>5</tex> </td> |
| − | <td> <tex> | + | <td> <tex>7</tex> </td> |
| − | <td> <tex> | + | <td> <tex>12</tex> </td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
| − | <td>''' | + | <td>''' ''<tex>\bar{Fys}</tex>'''</td> |
| − | <td> <tex> | + | <td> <tex>9</tex> </td> |
| − | <td> <tex> | + | <td> <tex>4</tex> </td> |
| − | <td> <tex> | + | <td> <tex>13</tex> </td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> '''Sum''' </td> | <td> '''Sum''' </td> | ||
| − | <td> <tex> | + | <td> <tex>14</tex> </td> |
| − | <td> <tex> | + | <td> <tex>11</tex> </td> |
| − | <td> <tex> | + | <td> <tex>25</tex> </td> |
</tr> | </tr> | ||
</table> | </table> | ||
Revisjonen fra 27. nov. 2012 kl. 07:44
Oppgave 1
a = -2 og punkt. (3,0)
<tex>0 = -2 \cdot 3 + b \\ b= 6 \\ dvs: \\ y=-2x+6</tex>
Oppgave 2
<tex>lg(2x+3) = 1 \\ 10^{lg(2x+3)} = 10^1 \\ 2x+3 =10 \\ x= \frac 72</tex>
Oppgave 3
<tex>\frac{(2x)^3x^2}{2^5x^{-1}} = 2^{3-5}x^{3+2+1}= \frac{x^6}{4}</tex>
Oppgave 4
<tex>\frac{x^2+6x+9}{x^2-9} = \frac{(x+3)(x+3)}{(x+3)(x-3)} = \frac{x+3}{x-3}</tex>
Oppgave 5
<tex> (\sqrt2 + \sqrt8)^2 = 2+2\sqrt2\sqrt8+8 = 18</tex>
Oppgave 6
a)
Nullpunkter:
f(x) = 0
<tex> x^2+2x-3 =0 \\ x= \frac{-2 \pm\sqrt{4+4 \cdot 3}}{2} \\ x=-3 \quad \vee \quad x=1</tex>
b)
<tex>f'(x) = 2x+2 \\ f'(x) = 0 \\ x= -1 \\ f(-1)=-4</tex>
f har et ekstremalpunkt i (-1,-4). Dette er et minimumspunkt da den deriverte er negativ for verdier mindre enn -1, og positiv for større verdier.
c)
Oppgave 7
<tex>(x+5)(x+3)-(x+5)82x+7)=0 \\ (x+5)(x+3-2x-7)=0 \\ (x+5)=0 \quad \vee \quad -x-4=0 \\ x=-5 \quad \vee \quad x=-4</tex>
Oppgave 8
| Bio | <tex>\bar{Bio}</tex> | Sum | |
| Fys | <tex>5</tex> | <tex>7</tex> | <tex>12</tex> |
| <tex>\bar{Fys}</tex> | <tex>9</tex> | <tex>4</tex> | <tex>13</tex> |
| Sum | <tex>14</tex> | <tex>11</tex> | <tex>25</tex> |
