# Find the following limits or state that they do not exist. lim_{hrightarrow0}frac{3}{sqrt{16+3h}+4}

Find the following limits or state that they do not exist.
$\underset{h\to 0}{lim}\frac{3}{\sqrt{16+3h}+4}$
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Evaluate:
$\underset{h\to 0}{lim}\frac{3}{\sqrt{16+3h}+4}$
Consider the given expression: $\underset{h\to 0}{lim}\frac{3}{\sqrt{16+3h}+4}$
$=\frac{3}{\sqrt{16+3\cdot 0}+4}$
$=\frac{3}{\sqrt{16}+14}$
$=\frac{3}{4+4}$
$=\frac{3}{8}$
Hence,$\underset{h\to 0}{lim}\frac{3}{\sqrt{16+3h}+4}=\frac{3}{8}$