El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$e^{x} \sin{\left(5 x \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = 0$$
$$x_{2} = - \frac{4 \pi}{5}$$
$$x_{3} = - \frac{3 \pi}{5}$$
$$x_{4} = - \frac{2 \pi}{5}$$
$$x_{5} = - \frac{\pi}{5}$$
$$x_{6} = \frac{\pi}{5}$$
$$x_{7} = \frac{2 \pi}{5}$$
$$x_{8} = \frac{3 \pi}{5}$$
$$x_{9} = \frac{4 \pi}{5}$$
$$x_{10} = \pi$$
Solución numérica$$x_{1} = -59.6902604182061$$
$$x_{2} = -13.8230076757951$$
$$x_{3} = -11.9380520836412$$
$$x_{4} = 30.159289474462$$
$$x_{5} = -25.7610597594363$$
$$x_{6} = -30.159289474462$$
$$x_{7} = -37.6991118430775$$
$$x_{8} = -81.6814089933346$$
$$x_{9} = -89.8495498926681$$
$$x_{10} = -21.9911485751286$$
$$x_{11} = -15.707963267949$$
$$x_{12} = 4.39822971502571$$
$$x_{13} = -32.0442450666159$$
$$x_{14} = 12.5663706143592$$
$$x_{15} = -55.9203492338983$$
$$x_{16} = -87.9645943005142$$
$$x_{17} = -65.9734457253857$$
$$x_{18} = 8.16814089933346$$
$$x_{19} = -98.0176907920015$$
$$x_{20} = -96.1327351998477$$
$$x_{21} = -94.2477796076938$$
$$x_{22} = 6.28318530717959$$
$$x_{23} = 11.9380520836412$$
$$x_{24} = -54.0353936417444$$
$$x_{25} = -85.4513201776424$$
$$x_{26} = -1.88495559215388$$
$$x_{27} = -49.6371639267187$$
$$x_{28} = 0$$
$$x_{29} = -42.7256600888212$$
$$x_{30} = -57.8053048260522$$
$$x_{31} = -67.8584013175395$$
$$x_{32} = -43.9822971502571$$
$$x_{33} = -47.7522083345649$$
$$x_{34} = -79.7964534011807$$
$$x_{35} = 20.1061929829747$$
$$x_{36} = -74.1415866247191$$
$$x_{37} = -33.9292006587698$$
$$x_{38} = -3.76991118430775$$
$$x_{39} = -52.1504380495906$$
$$x_{40} = 23.8761041672824$$
$$x_{41} = -27.6460153515902$$
$$x_{42} = -69.7433569096934$$
$$x_{43} = 18.2212373908208$$
$$x_{44} = -77.9114978090269$$
$$x_{45} = -45.867252742411$$
$$x_{46} = -8.16814089933346$$
$$x_{47} = 25.1327412287183$$
$$x_{48} = -42.0973415581032$$
$$x_{49} = 16.3362817986669$$
$$x_{50} = -76.026542216873$$
$$x_{51} = -86.0796387083603$$
$$x_{52} = -5.65486677646163$$
$$x_{53} = -23.8761041672824$$
$$x_{54} = 1.88495559215388$$
$$x_{55} = -64.0884901332318$$
$$x_{56} = 10.0530964914873$$
$$x_{57} = 28.2743338823081$$
$$x_{58} = -63.4601716025138$$
$$x_{59} = 21.9911485751286$$
$$x_{60} = -74.7699051554371$$
$$x_{61} = -35.8141562509236$$
$$x_{62} = -10.0530964914873$$
$$x_{63} = -99.9026463841554$$
$$x_{64} = -20.1061929829747$$
$$x_{65} = -91.734505484822$$