El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$x^{2} \cot{\left(\frac{21 x}{20} \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{10 \pi}{3}$$
$$x_{2} = - \frac{50 \pi}{21}$$
$$x_{3} = - \frac{10 \pi}{7}$$
$$x_{4} = - \frac{10 \pi}{21}$$
$$x_{5} = \frac{10 \pi}{21}$$
$$x_{6} = \frac{10 \pi}{7}$$
$$x_{7} = \frac{10 \pi}{3}$$
$$x_{8} = \frac{170 \pi}{21}$$
$$x_{9} = \frac{190 \pi}{21}$$
$$x_{10} = 10 \pi$$
$$x_{11} = - 10 i \log{\left(- \left(-1\right)^{\frac{4}{21}} \right)}$$
$$x_{12} = - 10 i \log{\left(- \left(-1\right)^{\frac{2}{7}} \right)}$$
Solución numérica$$x_{1} = 67.3198425769241$$
$$x_{2} = -88.2637936008561$$
$$x_{3} = -25.4319405290602$$
$$x_{4} = -55.3518705632487$$
$$x_{5} = 7.47998250854713$$
$$x_{6} = 1.49599650170943$$
$$x_{7} = -97.2397726111126$$
$$x_{8} = -34.4079195393168$$
$$x_{9} = -28.4239335324791$$
$$x_{10} = 85.2718005974372$$
$$x_{11} = -16.4559615188037$$
$$x_{12} = 52.3598775598299$$
$$x_{13} = -61.3358565700864$$
$$x_{14} = -7.47998250854713$$
$$x_{15} = -37.3999125427356$$
$$x_{16} = 37.3999125427356$$
$$x_{17} = 10.471975511966$$
$$x_{18} = 43.3838985495733$$
$$x_{19} = -94.2477796076938$$
$$x_{20} = 19.4479545222225$$
$$x_{21} = 46.3758915529922$$
$$x_{22} = -73.3038285837618$$
$$x_{23} = -4.48798950512828$$
$$x_{24} = -10.471975511966$$
$$x_{25} = 88.2637936008561$$
$$x_{26} = 100.231765614531$$
$$x_{27} = 16.4559615188037$$
$$x_{28} = -46.3758915529922$$
$$x_{29} = -13.4639685153848$$
$$x_{30} = -31.4159265358979$$
$$x_{31} = 61.3358565700864$$
$$x_{32} = 25.4319405290602$$
$$x_{33} = -49.367884556411$$
$$x_{34} = -100.231765614531$$
$$x_{35} = 31.4159265358979$$
$$x_{36} = -91.2557866042749$$
$$x_{37} = 4.48798950512828$$
$$x_{38} = -79.2878145905995$$
$$x_{39} = -43.3838985495733$$
$$x_{40} = 28.4239335324791$$
$$x_{41} = 94.2477796076938$$
$$x_{42} = -22.4399475256414$$
$$x_{43} = 64.3278495735053$$
$$x_{44} = -76.2958215871807$$
$$x_{45} = 97.2397726111126$$
$$x_{46} = 40.3919055461545$$
$$x_{47} = -85.2718005974372$$
$$x_{48} = 55.3518705632487$$
$$x_{49} = -52.3598775598299$$
$$x_{50} = -67.3198425769241$$
$$x_{51} = -82.2798075940184$$
$$x_{52} = -70.311835580343$$
$$x_{53} = -64.3278495735053$$
$$x_{54} = 13.4639685153848$$
$$x_{55} = 58.3438635666676$$
$$x_{56} = -40.3919055461545$$
$$x_{57} = -19.4479545222225$$
$$x_{58} = 22.4399475256414$$
$$x_{59} = 76.2958215871807$$
$$x_{60} = 91.2557866042749$$
$$x_{61} = 34.4079195393168$$
$$x_{62} = 49.367884556411$$
$$x_{63} = -58.3438635666676$$
$$x_{64} = 79.2878145905995$$
$$x_{65} = 73.3038285837618$$
$$x_{66} = 82.2798075940184$$
$$x_{67} = -1.49599650170943$$
$$x_{68} = 70.311835580343$$