now this can be solved using the std property ..or since it is 0/0 form so we can apply L'hospital rule..
I would go with the second method ..
Limx->4 Sin(x-4)/x-4)=> differentiate both the numerator and denominator ..we get
limx->4 Cos(x-4)/1 and now put x=4 and wet .= 1 as the answer