Question

In Problems 1– 6, find each limit

$\underset{x\to -6}{\lim }\sqrt{7-3x}$

Short answer

The value is$5$

Step-by-step solution

Step 1. Given information

We are given a limit function as $\underset{x\to -6}{\lim }\sqrt{7-3x}$

We need to find the value of the limit.

Step 2. Rewriting the limit function

The given function can be written as,

$$\begin{gathered} \underset{x\to -6}{\lim }\sqrt{7-3x}=\sqrt{\underset{x\to -6}{\lim }(7-3x)} \\ =\sqrt{\underset{x\to -6}{\lim }7-\underset{x\to -6}{\lim }3x} \\ =\sqrt{\underset{x\to -6}{\lim }7-3(-6)} \\ =\sqrt{7-3(-6)} \\ =\sqrt{25} \\ =5 \end{gathered}$$