### Home > APCALC > Chapter 3 > Lesson 3.3.3 > Problem3-119

3-119.

Compare the limit statements below. What do you notice? Homework Help ✎

1. $\lim\limits _ { h \rightarrow 0 } \large\frac { ( x + h + 1 ) ( x + h + 2 ) - ( x + 1 ) ( x + 2 ) } { h }$

1. $\lim\limits _ { h \rightarrow 0 } \large\frac { ( x + h + 1 ) ( x + h + 2 ) - ( x - h + 1 ) ( x - h + 2 ) } { 2 h }$

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

Your answer should include many observations, including:

They are both Defintions of the Derivative.

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

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

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.

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