El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\left(\sin{\left(\sqrt{5} x \right)} + \cos{\left(\sqrt{5} x \right)}\right) e^{- x} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{\sqrt{5} \pi}{20}$$
Solución numérica$$x_{1} = 34.7728329186516$$
$$x_{2} = 3.8636481020724$$
$$x_{3} = 13.6983887255294$$
$$x_{4} = 69.8969065738552$$
$$x_{5} = 44.6075735421086$$
$$x_{6} = 40.3926847034842$$
$$x_{7} = -17.2107960910498$$
$$x_{8} = 97.9961654980181$$
$$x_{9} = -0.351240736552036$$
$$x_{10} = -3.16116662896833$$
$$x_{11} = 60.0621659503982$$
$$x_{12} = -10.1859813600091$$
$$x_{13} = -31.2604255531312$$
$$x_{14} = 26.3430552414027$$
$$x_{15} = 83.9465360359367$$
$$x_{16} = -7.37605546759276$$
$$x_{17} = 27.7480181876109$$
$$x_{18} = 31.9629070262353$$
$$x_{19} = 86.756461928353$$
$$x_{20} = 88.1614248745611$$
$$x_{21} = -24.2356108220905$$
$$x_{22} = 46.0125364883168$$
$$x_{23} = 20.7232034565701$$
$$x_{24} = 78.3266842511041$$
$$x_{25} = 41.7976476496923$$
$$x_{26} = 72.7068324662715$$
$$x_{27} = 6.67357399448869$$
$$x_{28} = 82.5415730897285$$
$$x_{29} = -15.8058331448416$$
$$x_{30} = 92.3763137131856$$
$$x_{31} = 12.2934257793213$$
$$x_{32} = 36.1777958648597$$
$$x_{33} = 8.07853694069684$$
$$x_{34} = -1.75620368276018$$
$$x_{35} = 17.9132775641539$$
$$x_{36} = 64.2770547890226$$
$$x_{37} = 22.1281664027783$$
$$x_{38} = 58.6572030041901$$
$$x_{39} = 79.7316471973122$$
$$x_{40} = 100.806091390434$$
$$x_{41} = 93.7812766593937$$
$$x_{42} = 54.4423141655656$$
$$x_{43} = 55.8472771117738$$
$$x_{44} = 30.5579440800272$$
$$x_{45} = 2.45868515586425$$
$$x_{46} = 48.8224623807331$$
$$x_{47} = 68.4919436276471$$
$$x_{48} = -5.97109252138462$$
$$x_{49} = -25.6405737682987$$
$$x_{50} = 96.59120255181$$
$$x_{51} = 51.6323882731493$$
$$x_{52} = 62.8720918428145$$
$$x_{53} = -21.4256849296742$$
$$x_{54} = -29.8554626069231$$
$$x_{55} = 16.5083146179457$$
$$x_{56} = -20.0207219834661$$
$$x_{57} = 50.2274253269412$$
$$x_{58} = 74.1117954124797$$
$$x_{59} = -11.5909443062172$$