You can write the function after doing the LCM and you will have a function which has a (0/0) form...
So, you can easily apply the L'Hospital rule....
and apply the L'Hospital rule for once and see the magic... :-)
This wil be: ( Cos x - e^x )/( xe^x ) ---------------(a),and after applying the L'Hospital rule we will have
( - sin x - e^x ) / ( xe^x + e^x ) ------- just apply the differentiation on the numerator and denominator of the fraction for the exprression------(a)
And you can see now we don't have the (0/0) form and we can easily compute the limit by putting the limiting value of x tends to 0.
And you will have the answer as ( - 1).
Hope the answer will help you a bit.best of luck.