Step $1$

The limit to be evaluated is $\underset{x2}{lim}\frac{\sqrt[\phantom{2}]{x7}-3}{x-2}.$

By the direct substitution, we have the following.

$\underset{x2}{lim}\frac{\sqrt[\phantom{2}]{x7}-3}{x-2}=\frac{?}{0}$

Thus, the direct substitution results in $$ form.

$$ SKIP $($YOU CANNOT COME BACK$)$