Q. 30 - Calculus

Question

Calculate each of the limits in Exercises $29-70$.

$\underset{x\to 2}{\lim } (x - 1)(x + 1)(x + 5)$.

Step-by-Step Solution

Answer

The value of $\underset{x\to 2}{\lim } (x - 1)(x + 1)(x + 5)$ is, $21$.

Step 1 . Given information

$\underset{x\to 2}{\lim } (x - 1)(x + 1)(x + 5)$.

Step 2 . The limit is calculated as below:

$\underset{x\to 2}{\lim } (x - 1)(x + 1)(x + 5)=\underset{x\to 2}{\lim } (x - 1)\underset{x\to 2}{\lim }(x + 1)\underset{x\to 2}{\lim }(x + 5)$ [Product rule]

                                             $$\begin{gathered} =\left(2-1\right)\left(2+1\right)\left(2+5\right) \\ =\left(1\right)\left(3\right)\left(7\right) \\ =21 \end{gathered}$$