The set of all values of a for which limx→a([x−5]−[2x+2])=0, where [α] denotes the greatest integer less than or equal to α is equal to

Ltx→a([x−5]−[2x+2])=0 ⇒[a−5]−[2a+2]=0 ⇒[a−5]=[2a+2] Here, a∈[−7.5,−6.5) limit exist for a∈(-7.5, -6.5)

The set of all values of a for which limx→a([x−5]−[2x+2])=0, where [α] denotes the greatest integer less than or equal to α is equal to

Ltx→a([x−5]−[2x+2])=0 ⇒[a−5]−[2a+2]=0 ⇒[a−5]=[2a+2] Here, a∈[−7.5,−6.5) limit exist for a∈(-7.5, -6.5)

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The set of all values of a for which $\lim_{x \to a} ([x - 5] - [2 x + 2]) = 0$ , where $[α]$ denotes the greatest integer less than or equal to $α$ is equal to

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[-7.5, -6.5]

(-7.5, -6.5]

[-7.5, -6.5)

(-7.5, -6.5)

answer is D.

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$\underset{x \to a}{L t} ([x - 5] - [2 x + 2]) = 0 \Rightarrow [a - 5] - [2 a + 2] = 0 \Rightarrow [a - 5] = [2 a + 2] H e r e, a \in [- 7.5, - 6.5) l i m i t e x i s t f o r a \in (- 7.5, - 6.5)$

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The set of all values of a for which limx→a([x−5]−[2x+2])=0, where [α] denotes the greatest integer less than or equal to α is equal to

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The set of all values of a for which $\lim_{x \to a} ([x - 5] - [2 x + 2]) = 0$ , where $[α]$ denotes the greatest integer less than or equal to $α$ is equal to