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

Question
Limits and continuity
asked 2021-03-04
Find the following limits or state that they do not exist.
\(\lim_{h\rightarrow0}\frac{3}{\sqrt{16+3h}+4}\)

Answers (1)

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,\(\lim_{h\rightarrow0}\frac{3}{\sqrt{16+3h}+4}=\frac{3}{8}\)
0

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