Write the value of (xf(a) - af(x)/(x - a)[x ∈ a]

Question

Write the value of \(\lim\limits_{x \to a}\frac{xf(a)-af(x)}{x-a}\)

Answer 1

By definition of derivative we know that derivative of a function at a given real number say c is given by :

If somehow we got a form similar to that of in definition of derivative we can write it in a simpler form.

Using the definition of the derivative , we have –