Answer
\[2\]
Work Step by Step
Let \[L=\lim_{x\rightarrow 2}\frac{x^3}{\sqrt{x^2+x-2}}\]
Using the property : If $ \displaystyle\lim_{x\rightarrow a}f(x)=L_1,\; \displaystyle\lim_{x\rightarrow a}g(x)=L_2$ then
\[\lim_{x\rightarrow a}\frac{f(x)}{g(x)}=\frac{L_1}{L_2}\]
Since \[\lim_{x\rightarrow 2}(x^2+x-2)=(-2)^2+(-2)-2=0\]
\[L=\frac{\lim_{x\rightarrow 2}(x^3)}{\lim_{x\rightarrow 2}(\sqrt{x^2+x-2})}\]
Since polynomails are everyuwhere continuous therefore
\[\Rightarrow L=\frac{(2)^3}{\sqrt{(2)^2+2-2}}=\frac{8}{4}=2\]
