Evaluate:

\(\lim_{h\rightarrow0}\frac{3}{\sqrt{16+3h}+4}\)

Consider the given expression: \(\lim_{h\rightarrow0}\frac{3}{\sqrt{16+3h}+4}\)

\(=\frac{3}{\sqrt{16+3\cdot0}+4}\)

\(=\frac{3}{\sqrt{16}+14}\)

\(=\frac{3}{4+4}\)

\(=\frac{3}{8}\)

Hence,\(\lim_{h\rightarrow0}\frac{3}{\sqrt{16+3h}+4}=\frac{3}{8}\)

\(\lim_{h\rightarrow0}\frac{3}{\sqrt{16+3h}+4}\)

Consider the given expression: \(\lim_{h\rightarrow0}\frac{3}{\sqrt{16+3h}+4}\)

\(=\frac{3}{\sqrt{16+3\cdot0}+4}\)

\(=\frac{3}{\sqrt{16}+14}\)

\(=\frac{3}{4+4}\)

\(=\frac{3}{8}\)

Hence,\(\lim_{h\rightarrow0}\frac{3}{\sqrt{16+3h}+4}=\frac{3}{8}\)