Q. 26 - Calculus

Question

Calculate the limits in Exercises 25–28, using only the continuity of linear and power functions and the limit rules. Cite each limit rule that you apply. 

$\underset{x\to -1}{lim} \frac{x-1}{(x+4)(x+2)}$

Step-by-Step Solution

Answer

$\underset{x\to -1}{lim} \frac{x-1}{(x+4)(x+2)}=\frac{2}{3}$

Step 1. Given information.

We have to calculate the limit of the given function.

Function is:

$\underset{x\to -1}{lim} \frac{x-1}{(x+4)(x+2)}$

Step 2. Calculate the limit

The limit of the function can be calculated as:

$\begin{array}{r}\underset{x\to -1}{lim} \frac{x-1}{(x+4)(x+2)}\\ =\frac{\underset{x\to -1}{lim} (x-1)}{\underset{x\to -1}{lim} (x+4)(x+2)}\\ =\frac{\underset{x\to -1}{lim} (x-1)}{\underset{x\to -1}{lim} (x+4)\underset{x\to -1}{lim} (x+2)}\\ =\frac{(-1)-1}{(-1+4)(-1+2)}\\ =\frac{-1-1}{3\left(1\right)}\\ =\frac{-2}{3}\\ =\frac{2}{3}\end{array}$