The set of all values of a for which lim x→a ([x - 5] - [2x + 2]), where [∝] denotes the greater integer less than or equal to ∝ is equal to ​

Question

The set of all values of a for which \(\lim\limits_{x\to a} ([x-5]-[2x +2])\), where [∝] denotes the greater integer less than or equal to ∝ is equal to

(1) (– 7.5, –6.5)

(2) (– 7.5, –6.5]

(3) [– 7.5, –6.5]

(4) [– 7.5, –6.5)

Answer 1

Correct option is (1) (– 7.5, –6.5)

Comments

The Equation is satisfied at x=7.5.

look!
--->[-7.5]-[2(-7.5)]=7
--->-8 - (-15) = 7
---> 15-8 = 7
---> 7 = 7
---> RHS = LHS, bro what were you thinking!