Suppose f and g are continuous functions such that g(2) = 6 and lim x → 2 [3f(x) + f(x)g(x)] = 36. find f(2).

Answer is      ====    with  since  is a continuous function, then the limit of g(x) as x approaches 2  should be the same as the value of the function g at 2. this is basically the definition of continuity.    we can use limit laws to evaluate the given limit equation.    limit law:   , so    for the boxed portion above, we apply the limit law      for the boxed portion above, we apply the limit law      we established before that since  is continuous,      there are like terms on the left side (coefficients on  ); we can add them and then divide by 9    so  .since  is a continuous function, by the definition of continuity:     so