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JEE Mains · Maths · STD 11 - 12. limits
The set of all values of \(a\) for which \(\operatorname{Lim}_{x \rightarrow a}([x-5]-[2 x+2])=0\), where \([\propto]\) denotes the greater integer less than or equal to \(\propto\) is equal to
- A \((-7.5,-6.5)\)
- B \((-7.5,-6.5]\)
- C \([-7.5,-6.5]\)
- D \([-7.5,-6.5)\)
Answer & Solution
Correct Answer
(A) \((-7.5,-6.5)\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow a}(\lfloor x-5]-\lfloor 2 x+2\rfloor)=0\) \(\lim _{x \rightarrow a}([x]-5-[2 x]-2)=0\) \(\lim _{x \rightarrow a}([x]-[2 x])=7\) \({[a]-[2 a]=7}\) \(a \in I, \quad a=-7\) \(a \notin I, \quad a=I+f\) \(\text { Now, }[a]-[2 a]=7\) \(\quad-I-[2 f]=7\)…
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