Respuestas - Sección 5.1

Aquí encontrarás la norma de las funciones de los ejercicios 7 a 12

  1. ∥sen(2n+1)x∥=π2\hspace{0.5cm} \left\| sen\left(2n+1\right)x \right\|=\dfrac{\sqrt\pi}{2}

  2. ∥cos(2n+1)x∥=π2\hspace{0.5cm} \left\| cos{\left(2n+1\right)}x \right\|=\dfrac{\sqrt\pi}{2}

  3. ∥sennx∥=π2\hspace{0.5cm} \left\| sennx \right\|=\dfrac{\sqrt\pi}{2}

  4. ∥sennπpx∥=p2\hspace{0.5cm} \left\| sen\dfrac{n\pi}{p}x \right\|=\sqrt{\dfrac{p}{2}}

  5. ∥1∥=p      ∥cosnπpx∥=p2\hspace{0.5cm} \left\| 1 \right\|=\sqrt p \;\;\;\left\| cos{\dfrac{n\pi}{p}}x \right\|=\sqrt{\dfrac{p}{2}}

  6. ∥1∥=2p      ∥cosnπpx∥=p      ∥sennπpx∥=p\hspace{0.5cm} \left\| 1 \right\|=\sqrt{2p} \;\;\;\left\| cos{\dfrac{n\pi}{p}}x \right\|=\sqrt{p} \;\;\;\left\| sen{\dfrac{n\pi}{p}}x \right\|=\sqrt{p}