Find the limits lim_{xrightarrow-3}frac{2-sqrt{x^2-5}}{x+3}

Question
Limits and continuity
asked 2020-10-23
Find the limits
\(\lim_{x\rightarrow-3}\frac{2-\sqrt{x^2-5}}{x+3}\)

Answers (1)

2020-10-24
Given Data
The limit is \(\lim_{x\rightarrow-3}\frac{2-\sqrt{x^2-5}}{x+3}\)
Solve the given limit expression,
\(L=\lim_{x\rightarrow-3}\frac{2-\sqrt{x^2-5}}{x+3}\)
\(=\frac{2-\sqrt{(-3)^2-5}}{-3+3}\)
\(=\frac{2-\sqrt{9-5}}{0}\)
\(=\infty\)
The value of limit is \(\infty\) so it means that the sequence diverge.
Hence the limit does not exists and sequence diverge.
0

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