We have to find the value of lim x--> pi[ sin 5x / sin x]
We see that substituting x with pi gives us the form 0/0 which is indeterminate. We can use therefore use l'Hopital's rule and use the derivative of the numerator and the denominator
lim x--> pi [sin 5x / sin x]
=> lim x--> pi [ 5* cos 5x / cos x]
substtuting x = pi , now gives
The required value of lim x--> pi[ sin 5x / sin x] is 5.