Evaluate the following limits. lim_{xrightarrow2}frac{sin(x-2)}{x^2-4}

Question
Limits and continuity
asked 2021-01-08
Evaluate the following limits.
\(\lim_{x\rightarrow2}\frac{\sin(x-2)}{x^2-4}\)

Answers (1)

2021-01-09
Given limit is
\(\lim_{x\rightarrow2}\frac{\sin(x-2)}{x^2-4}\)
Solve,
\(\lim_{x\rightarrow2}\frac{\sin(x-2)}{x^2-4}=\lim_{x\rightarrow2}\frac{\sin(x-2)}{(x-2)(x+2)}\)
\(=\lim_{x\rightarrow2}(\frac{\sin(x-2)}{(x-2)})\lim_{x\rightarrow2}(\frac{1}{x+2})\)
\(=1\times(\frac{1}{4})\) \) \(=\frac{1}{4}\)
0

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