Alguien me explica esto senx = x ^ 2 como lo resuelvo gracias?

1) Primero debemos recordar que<img src="https://tex.z-dn.net/?f=%5Csin%3A%20%5Cmathbb%20R%5Cto%20%5B-1%2C1%5D" /> y como<img src="https://tex.z-dn.net/?f=x%5E2%5Cgeq%200%20~%2C~%20%5Cforall%20x%5Cin%20%5Cmathbb%7BR%7D" />, deducimos que<img src="https://tex.z-dn.net/?f=x%5Cin%5B0%2C1%5D" />

2) Ahora veamos esta función<img src="https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2-%5Csin%20x" /> debemos aplicar el método de Newton - Rhapson para los <img src="https://tex.z-dn.net/?f=x_k%5Cin%5B0%2C1%5D" />.

Empecemos con<img src="https://tex.z-dn.net/?f=x_1%3D1" />

<img src="https://tex.z-dn.net/?f=x_2%3Dx_1-%5Cdfrac%7Bf%28x_1%29%7D%7Bf%27%28x_1%29%7D%3Dx_1-%5Cdfrac%7Bx_1%5E2-%5Csin%20x_1%7D%7B2x_1-%5Ccos%20x_1%7D%5C%5C%20%5C%5C%20%5C%5C%0Ax_2%3D1-%5Cdfrac%7B1%5E2-%5Csin%201%7D%7B2-%5Ccos%201%7D%5C%5C%20%5C%5C%20%5C%5C%0Ax_2%5Capprox%200.8913959953%5C%5C%20%5C%5C%0A------------------------------%5C%5C%20%5C%5C%0Ax_3%3Dx_2-%5Cdfrac%7Bf%28x_2%29%7D%7Bf%27%28x_2%29%7D%5C%5C%20%5C%5C%0Ax_3%5Capprox%200.8769848447%5C%5C%20%20%5C%5C%0A------------------------------%5C%5C%20%5C%5C%0Ax_4%3Dx_3-%5Cdfrac%7Bf%28x_3%29%7D%7Bf%27%28x_3%29%7D%5C%5C%20%5C%5C%0Ax_4%5Capprox%200.8767262984%5C%5C%20%5C%5C%0A------------------------------%5C%5C%20%5C%5C%0Ax_5%3Dx_4-%5Cdfrac%7Bf%28x_4%29%7D%7Bf%27%28x_4%29%7D%5C%5C%20%5C%5C%0Ax_5%5Capprox%200.8767262153%5C%5C%20%5C%5C%0A" />

<img src="https://tex.z-dn.net/?f=%5Ctexttt%7BHasta%20aqu%5C%27i%20el%20error%20es%20%7D%0AE%3D%5Cleft%7C1-%5Cdfrac%7Bx_4%7D%7Bx_5%7D%5Cright%7C%5Capprox%209.48%5Ctimes10%5E%7B-8%7D%0A" />

La solución trivial es x = 0, por ende la solución es<img src="https://tex.z-dn.net/?f=x%5Cin%5C%7B0~%2C~~%200.8767262153%5C%7D" />.