lim(x->a) [(xsina-asinx) /(x-a) ]=sina-acosa........ PROOF

lim [ (xsin(a) - asin(x)) / (x - a) ] x -> a We have to use L`Hospital`s rule to solve this. This means we take the derivative of each of the top and bottom and calculate a new limit. Keep in mind that "a" is a constant and can be differentiated accordingly as a constant. lim [ (sin(a) - acos(x)) / (1) ] x -> a Now, we can safely plug in the value of a, giving us sin(a) - a cos(a) And this should be our answer.

Approved