o find f (a), we will use the formula f0-fa) a t-a f (a) lim Since ft)- 9t+9 we have t+6 9t+99+9 f '(a) lim+6 a+6 x-at-a Putting the fractions in the numerator over a common denominator and simplifying, we have t+6 a+6 (t +6)(a +6) ta + 9a + 54t + 54-9at-9t-54a-54 t +6)(a+6) 45t-45 (t 6)(a 6) 45 a Part 2 of 3 Substituting this simplified numerator back into the limit, factoring and canceling common factors, we have 9t+9 9a+9 f'(a)= lim t+ 6 at 6 5t 45a lim t-a (t + 6)(a + 6)( (a +6)