\(\displaystyle\lim_{{{x}\rightarrow{4}}}{x}^{{{2}}}+\sqrt{{\lim_{{{x}\rightarrow{4}}}{7}-\lim_{{{x}\rightarrow{4}}}{x}}}\) Apply the Sum Law, Difference Law, and Root Law

\(\displaystyle{\left({4}\right)}^{{{2}}}+\sqrt{{{7}-{4}}}\) Plug in the corresponding values

\(\displaystyle{f{{\left({4}\right)}}}={16}+\sqrt{{{3}}}\) Evaluate

continuous f(4) is defined and equal to \(\displaystyle{16}+\sqrt{{{3}}}\) at \(x=4\), thus it is continuous at that point.