Answer
$\displaystyle \frac{3}{2}$
Work Step by Step
$\displaystyle \lim_{x\rightarrow 2}\sqrt{2x^{2}+13x-2}=$
... Law 11, $\displaystyle \lim_{x\rightarrow a}\sqrt[n]{f(x)}=\sqrt[n]{\lim_{x\rightarrow a}f(x)}$
= $\sqrt{\lim_{x\rightarrow 2}\dfrac{2x^{2}+1}{3x-2}}$
... Law 5, quotient
$=\sqrt{\dfrac{\lim_{x\rightarrow 2}(2x^{2}+1)}{\lim_{x\rightarrow 2}(3x-2)}}$
...Laws 1 (sum), 2 (difference), and 3 (constant multiple)
$=\sqrt{\dfrac{\lim_{x\rightarrow 2}2x^{2}+\lim_{x\rightarrow 2}1}{\lim_{x\rightarrow 2}3x-\lim_{x\rightarrow 2}2}}$
... Laws 9: $( \displaystyle \lim_{x\rightarrow a}x^{n}=a^{n})$, 8: ( $\displaystyle \lim_{x\rightarrow a}x=a$), and 7:($\displaystyle \lim_{x\rightarrow a}c=c$)
$=\sqrt{2(2)^{2}+13(2)-2}$
$=\sqrt{\dfrac{9}{4}}$
$=\displaystyle \frac{3}{2}$
