En resumen

<img src="https://tex.z-dn.net/?f=%5Clim%20_%7Bx%5Cto%20%5C%3A%5Cpi%20%7D%5Cleft%28%5Cfrac%7B1-%5Csin%20%5Cleft%28%5Cfrac%7Bx%7D%7B2%7D%5Cright%29%7D%7B%5Cpi%20-x%7D%5Cright%29" /> Se aplica la regla de L´Hopital : <img src="https://tex.z-dn.net/?

Mejor respuesta

Pachupachu
8

<img src="https://tex.z-dn.net/?f=%5Clim%20_%7Bx%5Cto%20%5C%3A%5Cpi%20%7D%5Cleft%28%5Cfrac%7B1-%5Csin%20%5Cleft%28%5Cfrac%7Bx%7D%7B2%7D%5Cright%29%7D%7B%5Cpi%20-x%7D%5Cright%29" />

Se aplica la regla de L´Hopital :

<img src="https://tex.z-dn.net/?f=%3D%5Clim%20_%7Bx%5Cto%20%5C%3A%5Cpi%20%7D%5Cleft%28%5Cfrac%7B-%5Cfrac%7B1%7D%7B2%7D%5Ccos%20%5Cleft%28%5Cfrac%7Bx%7D%7B2%7D%5Cright%29%7D%7B-1%7D%5Cright%29" />

Se simplifica :

<img src="https://tex.z-dn.net/?f=%3D%5Clim%20_%7Bx%5Cto%20%5C%3A%5Cpi%20%7D%5Cleft%28%5Cfrac%7B%5Ccos%20%5Cleft%28%5Cfrac%7Bx%7D%7B2%7D%5Cright%29%7D%7B2%7D%5Cright%29" />

Se sutituye la variable :

<img src="https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Ccos%20%5Cleft%28%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%7D%7B2%7D%3D0" />.