AP EAMCET · Maths · Limits
If \(g(x)=\frac{x}{[x]}\) for \(\mathrm{x}>2\), then \(\lim _{x \rightarrow 2} \frac{g(x)-g(2)}{x-2}\) is equal to
- A \(-1\)
- B \(0\)
- C \(\frac{1}{2}\)
- D \(2\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Given, \(g(x)=\frac{x}{[x]}\) When, \(x>2\), then \([x]=2 \Rightarrow g(x)=\frac{x}{2}\) Now, \(\quad \lim _{x \rightarrow 2} \frac{g(x)-g(2)}{x-2}=\lim _{x \rightarrow 2} \frac{\frac{x}{2}-1}{x-2}\)…
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