Question

Evaluate the limit and justify each step by indicating the appropriate limit law(s).

$\underset{u\to -2}{\lim }\sqrt{u^4+3u+6}$

Short answer

The value of limit of the given function is$4.$

Step-by-step solution

Step 1. Given information.

The limit of function is given here,

$\underset{u\to -2}{\lim }\sqrt{u^4+3u+6}$

Step 2. Formula used.

The given function can be find by direct substitution

Step 3. Simplification.

Given$\underset{u\to -2}{\lim }\sqrt{u^4+3u+6}$

$\begin{array}{c}\underset{u\to -2}{\lim }\sqrt{u^4+3u+6}=\sqrt{{(-2)}^4+3\times -2+6}\\ =\sqrt{16-6+6}\\ =\sqrt{16}\\ =4\end{array}$

Therefore, our final answer is$4.$