limit x tends to 0

e^(-x²/2) – cosx = ?

x³sinx

answer is  1/12

best method for these type of questions is series expansion

when we use series of e^x , sinx , cosx , value of limit will be coefficient of x⁴ , as x is tending to 0

and all other powers will become 0

so answer is 1/12

 

approve if useful

you can solve the given question by using lhospital
very useful and time saving rather series expansion
0/0 form is obtained diffrentiate until you are out of the form
finally put x=0
the answer will be 1/12

approve if useful