El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\left(- \sin{\left(\frac{\sqrt{15} x}{2} \right)} - \cos{\left(\frac{\sqrt{15} x}{2} \right)}\right) e^{\frac{x}{2}} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{\sqrt{15} \pi}{30}$$
Solución numérica$$x_{1} = -16.6286925714918$$
$$x_{2} = 12.5729138955182$$
$$x_{3} = -10.139446689934$$
$$x_{4} = -6.89482374915514$$
$$x_{5} = 17.4398483066865$$
$$x_{6} = -78.2765284462907$$
$$x_{7} = -47.4526105088913$$
$$x_{8} = -36.0964302161651$$
$$x_{9} = -60.4311022720068$$
$$x_{10} = -52.3195449200596$$
$$x_{11} = -3.65020080837625$$
$$x_{12} = -68.542659623954$$
$$x_{13} = 57.9976350664227$$
$$x_{14} = -76.6542169759013$$
$$x_{15} = -104.233511972522$$
$$x_{16} = 40.1522088921388$$
$$x_{17} = -79.8988399166802$$
$$x_{18} = 49.8860777144754$$
$$x_{19} = -11.7617581603235$$
$$x_{20} = -63.6757252127857$$
$$x_{21} = 6.08366801396042$$
$$x_{22} = -70.1649710943435$$
$$x_{23} = 23.9290941882443$$
$$x_{24} = 48.263766244086$$
$$x_{25} = -42.5856760977229$$
$$x_{26} = -0.405577867597361$$
$$x_{27} = 30.4183400698021$$
$$x_{28} = 15.8175368362971$$
$$x_{29} = 51.5083891848649$$
$$x_{30} = -19.8733155122707$$
$$x_{31} = 41.7745203625282$$
$$x_{32} = 33.662963010581$$
$$x_{33} = -34.4741187457757$$
$$x_{34} = -13.3840696307129$$
$$x_{35} = 7.70597948434986$$
$$x_{36} = -73.4095940351224$$
$$x_{37} = 54.7530121256438$$
$$x_{38} = -32.8518072753863$$
$$x_{39} = -45.8302990385018$$
$$x_{40} = 4.46135654357097$$
$$x_{41} = -29.6071843346074$$
$$x_{42} = -89.6327087390168$$
$$x_{43} = 28.7960285994126$$
$$x_{44} = 46.6414547736965$$
$$x_{45} = -26.3625613938285$$
$$x_{46} = -96.1219546205746$$
$$x_{47} = -53.941856390449$$
$$x_{48} = 38.5298974217493$$
$$x_{49} = -44.2079875681124$$
$$x_{50} = -62.0534137423963$$
$$x_{51} = 25.5514056586338$$
$$x_{52} = 59.6199465368121$$
$$x_{53} = -97.744266090964$$
$$x_{54} = 14.1952253659076$$
$$x_{55} = -71.7872825647329$$
$$x_{56} = 43.3968318329176$$
$$x_{57} = -8.51713521954458$$
$$x_{58} = -55.5641678608385$$
$$x_{59} = 22.3067827178549$$
$$x_{60} = 56.3753235960332$$
$$x_{61} = 66.1091924183699$$
$$x_{62} = -94.4996431501852$$
$$x_{63} = -2.02788933798681$$
$$x_{64} = -88.0103972686274$$
$$x_{65} = -86.3880857982379$$
$$x_{66} = -21.4956269826601$$
$$x_{67} = -18.2510040418813$$
$$x_{68} = -39.341053156944$$
$$x_{69} = 32.0406515401915$$
$$x_{70} = -81.5211513870696$$
$$x_{71} = -99.3665775613535$$
$$x_{72} = -27.9848728642179$$
$$x_{73} = 20.6844712474654$$
$$x_{74} = -37.7187416865546$$