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

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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.

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