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JEE Main202324 Jan 2023Evening ShiftMathematicsLimitsActual

The set of values of a for which lim x → a x - 5 - 2 x + 2 = 0 , where, ζ denotes the greatest integer less than or equal to ζ is equal to

Options

  1. A- 7 . 5 , - 6 . 5
  2. B( - 7 . 5 , - 6 . 5 ]
  3. C- 7 . 5 , - 6 . 5
  4. D[ - 7 . 5 , - 6 . 5 )

Correct answer

A. - 7 . 5 , - 6 . 5

Step-by-step solution

We have, lim x → a x - 5 - 2 x + 2 = 0 ⇒ lim x → a x - 5 - 2 x - 2 = 0 ⇒ lim x → a x - 2 x - 7 = 0 ⇒ lim x → a x - 2 x = 7 Now when a ∈ I (integer) then a - 2 a = 7 ⇒ a = - 7 Now when a ∈ I + f where f is fraction, So, I + f - 2 I + 2 f = 7 ⇒ I + f - 2 I - 2 f = 7 ⇒ I + 0 - 2 I - 2 f = 7 ⇒ - I - 2 f = 7 Now taking case 1 when f ∈ 0 , 1 2 Then ⇒ - I - 0 = 7 ⇒ I = - 7 ⇒ a ∈ - 7 , - 6 . 5 Now taking case 2 when

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