Compare the limit statements below. What do you notice?

1. What do they have in common? How are they different?

   Hint (a):

   Your answer should include many observations, including:

   Answer 1(a):

   They are both Defintions of the Derivative.

   Answer 2(a):

   i. uses Hana's Method.
   ii. uses Hanah's Method.

   Answer 3(a):

   In both cases, the function that is being differentiated is $f(x) = (x + 1)(x + 2)$.

   Answer 4(a):

   Once $f(x)$ is determined, both can be evaluated using the Power rule, avoiding lengthy Algebraic manipulation.

2. Evaluate these limits using any method you choose.

   Hint (b):

   i. Refer to hints in problem 3-64.
   ii. Refer to hints in problem 3-92.