solve the limit of the function f(x)=sin5x/sinx if x --> pi

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

(5*-1)/ (-1)

=>
5

The required value of lim x--> pi[
sin 5x / sin x] is 5.