Forskjell mellom versjoner av «R1 2008 høst LØSNING»
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<p></p> <tex>\quad \quad x^3-3x^2-x+3: (x+1) = x^2-4x+3 \\ -(x^3 +x^2) \\ \quad \quad\quad\quad \quad -4x^2-x \\ \quad \quad -(-4x^2-4x) \\ \quad \quad\quad \quad\quad \quad\quad \quad\quad \quad -(3x+3)\\ \quad \quad\quad \quad \quad \quad\quad \quad\quad \quad\quad \quad\quad\quad \quad \quad 0 </tex> | <p></p> <tex>\quad \quad x^3-3x^2-x+3: (x+1) = x^2-4x+3 \\ -(x^3 +x^2) \\ \quad \quad\quad\quad \quad -4x^2-x \\ \quad \quad -(-4x^2-4x) \\ \quad \quad\quad \quad\quad \quad\quad \quad\quad \quad -(3x+3)\\ \quad \quad\quad \quad \quad \quad\quad \quad\quad \quad\quad \quad\quad\quad \quad \quad 0 </tex> | ||
<p></p> | <p></p> | ||
+ | <tex>x^2-4x+3 = 0 \\ x= \frac {4 \pm \sqrt{16-12}}{2} = \frac{4 \pm 2}{2} \\ x = 1 \vee x=3 \\ f(x)= x^3-3x^2-x+1 = (x+1)(x-1)(x-3)</tex> | ||
2) | 2) | ||
<p></p> | <p></p> |
Revisjonen fra 20. sep. 2012 kl. 05:41
Oppgave 1:
a)
1)<tex>f(x)=3e^{2x}, \quad f'(x) = 3 \cdot 2 e^{2x} = 6e^{2x}</tex>
2)<tex>h(x)=x \cdot lnx, \quad h'(x) = lnx + x \cdot \frac 1x = lnx + 1 </tex>
b)
l går gjennom A(1,2) og B(3,7), <tex> \vec{AB}=[2,5]</tex>
1)Parameterfremmstilling:<tex> l: \left [ x = 1+2t \\ y = 2 + 5t \right]</tex>
2) Skjæring med x-akse, y = 0:<tex>t = - \frac 25 \Rightarrow x = \frac 15, \quad \quad ( \frac 15,0)</tex>
Skjæring med y-akse, x = 0:<tex>t = - \frac 12 \Rightarrow y = -\frac 12, \quad \quad (0,- \frac 12)</tex>
c)
1)<tex>f(-1) = (-1)^3 - 3 \cdot (-1)^2 - (-1)+3 = -1-3+1+3 = 0 \quad</tex> dvs.f(x) er delelig med (x-(-1))
<tex>\quad \quad x^3-3x^2-x+3: (x+1) = x^2-4x+3 \\ -(x^3 +x^2) \\ \quad \quad\quad\quad \quad -4x^2-x \\ \quad \quad -(-4x^2-4x) \\ \quad \quad\quad \quad\quad \quad\quad \quad\quad \quad -(3x+3)\\ \quad \quad\quad \quad \quad \quad\quad \quad\quad \quad\quad \quad\quad\quad \quad \quad 0 </tex>
<tex>x^2-4x+3 = 0 \\ x= \frac {4 \pm \sqrt{16-12}}{2} = \frac{4 \pm 2}{2} \\ x = 1 \vee x=3 \\ f(x)= x^3-3x^2-x+1 = (x+1)(x-1)(x-3)</tex> 2)
d)
1)
2)
e)
1)
2)
Oppgave 2:
a)
b)
c)
DEL TO