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

Question
Limits and continuity
Find the following limits or state that they do not exist.
$$\lim_{h\rightarrow0}\frac{3}{\sqrt{16+3h}+4}$$

2021-03-05
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,$$\lim_{h\rightarrow0}\frac{3}{\sqrt{16+3h}+4}=\frac{3}{8}$$

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