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Matteprøve (Kapittel 4 & 5 (Volum/areal (Pyramide (\(\left|\frac{1}{3}…

- - - - \(\left(x-a\right)^{2}+\left(y-b\right)^{2}+\left(z-c\right)^{2}=r^{2}\)
    - - \(\left(\vec{a}\times\vec{b}\right)\cdot\vec{AB}=\vec{n}\cdot\vec{AB}\)
  - - - \(\left|\frac{1}{3}\left(\vec{a}\times\vec{b}\right)\cdot\vec{c}\right|\)
    - - \(\left|\frac{1}{6}\left(\vec{a}\times\vec{b}\right)\cdot\vec{c}\right|\)
    - - \(\left|\left(\vec{a}\times\vec{b}\right)\cdot\vec{c}\right|\)
    - - \(\left|\vec{a}\times\vec{b}\right|\)
    - - \(\frac{1}{2}\left|\vec{a}\times\vec{b}\right|\)
  - - - \(\theta \leq 90^{\circ} \rightarrow \underline{\underline{\theta}}\)
      - \(\theta > 90^{\circ} \rightarrow \underline{\underline{180^{\circ}-\theta}}\)
    - - \(\theta>90^{\circ} \rightarrow \underline{\underline{\theta-90^{\circ}}}\)
      - \(\theta \leq 90^{\circ} \rightarrow \underline{\underline{90^{\circ}-\theta}}\)
  - - - \(\frac{\left|\vec{n}\cdot\vec{AP}\right|}{\left|\vec{n}\right|}\)
    - - \(\left|\vec{AS}\right|\)
    - - \(\frac{\left|\vec{l}\times\vec{AL}\right|}{\left|\vec{l}\right|}\)
    - - \(\frac{\left|\vec{n}\cdot\vec{AS}\right|}{\left|\vec{n}\right|}\)
  - - - \(\begin{cases}x=x_{0}+a_{1}t\\y=y_{0}+a_{2}t\\z=z_{0}+a_{3}t\end{cases}\)
    - - \(\begin{cases}x=x_{0}+a_{1}s+b_{1}t\\y=y_{0}+a_{2}s+b_{2}t\\z=z_{0}+a_{3}s+b_{3}t\end{cases}\)
- - - - a er lengden fra likevektslinjen til et ekstremalpunkt
      - c er forskyvelsen i x-aksen fra likevektslinjen(sinus) eller toppunktet (cosinus)
      - d er lengden fra x-aksen til likevektslinjen
      - k er frekvens: \(frekvens=\frac{2\pi}{periode}\)
- - - - \(\pi\int_{a}^{b}\left(f\left(x\right)\right)^{2}dx\)
    - - \(\int_{a}^{b}\left(f\left(x\right)\right)dx\)
    - - \(\int_{a}^{b}\left(f\left(x\right)-g\left(x\right)\right)dx\)
- - - - \(y\cdot e^{\int\left(p\left(x\right)dx\right)}=\int\left(q\left(x\right)\cdot e^{\int\left(p\left(x\right)dx\right)}dx\right)\)
    - - \(y'dx=dy\)
      - \(\int\left(a\left(y\right)b\left(y'\right) dx\right)=\int\left(c\left(x\right)dx\right)\)
  - - - en løsning
        
        \(y=e^{r_{1}x}\left(C+Dx\right)\)
      - \(r=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\)
      - to løsninger
        
        \(y=Ce^{r_{1}x}+De^{r_{2}x}\)
    - - \(r=p\pm q\sqrt{-1}\)
      - \(y=e^{px}\left(C\cos\left(qx\right)+D\sin\left(qx\right)\right)\)