please solve this que and send me whole solution

for these type of questions best approach is SERIES EXPANSION  the answer will be 3 

as u expand the series of cosx and e^x and multiply the atarting coefficient u get x³ and then so on but we consider only first term and value of limit is given finite so value of n=3  so that it can cancel the upper x³ and make the value of limit finite.  

approve if useful