Answer
4
Work Step by Step
$\displaystyle \lim_{u\rightarrow-2}\sqrt{u^{4}+3u+6}$
...Law 11: $\displaystyle \lim_{x\rightarrow a}\sqrt[n]{f(x)}=\sqrt[n]{\lim_{x\rightarrow a}f(x)}$
$=\sqrt{\lim_{u\rightarrow-2}(u^{4}+3u+6)}$
...Laws 1 (sum), 2 (difference), and 3 (constant multiple)
$=\sqrt{\lim_{u\rightarrow-2}u^{4}+3\lim_{u\rightarrow-2}u+\lim_{u\rightarrow-2}6}$
Laws 9: $( \displaystyle \lim_{x\rightarrow a}x^{n}=a^{n})$, 8: ( $\displaystyle \lim_{x\rightarrow a}x=a$), and 7:($\displaystyle \lim_{x\rightarrow a}c=c$)
$=\sqrt{(-2)^{4}+3(-2)+6}$
$=\sqrt{16-6+6}$
$=\sqrt{16}$
$=4$
