TS EAMCET · Maths · Limits
If \(l_1=\lim _{x \rightarrow 2^{+}}(x+[x]), l_2 \lim _{x \rightarrow 2^{-}}(2 x-[x])\) and \(l_3=\lim _{x \rightarrow \pi / 2} \frac{\cos x}{(x-\pi / 2)}\), then :
- A \(l_1 < l_2 < l_3\)
- B \(l_2 < l_3 < l_1\)
- C \(l_3 < l_2 < l_1\)
- D \(l_1 < l_3 < l_2\)
Answer & Solution
Correct Answer
(C) \(l_3 < l_2 < l_1\)
Step-by-step Solution
Detailed explanation
\(l_1=\lim _{x \rightarrow 2^{+}} x+[x]\) \(=\lim _{h \rightarrow 0} 2+h+[2+h]=4\) \(l_2=\lim _{x \rightarrow 2^{-}}(2 x-[x])\) \(=\lim _{h \rightarrow 0}\{2(2-h)-[2-h]\}\) \(=\lim _{h \rightarrow 0}\{2(2-h)-1\}=4-1=3\)…
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