If
where, denotes the greatest integer less than or equal to , then equals
where, denotes the greatest integer less than or equal to , then equals
- A.(a) 1
- B.(b) 0
- C.(c)
- D.(d) None of these
Show answer and solution
Correct option: D
Solution
For x → 0⁺, [x] = 0, so f(x) = 0, giving right-hand limit = 0.
For x → 0⁻, [x] = -1, so f(x) = sin(-1)/(-1) = sin(1), giving left-hand limit = sin(1).
Since sin(1) ≠ 0, the left-hand and right-hand limits are unequal, so the limit does not exist — which is none of the values listed (1, 0, or -1).
For x → 0⁻, [x] = -1, so f(x) = sin(-1)/(-1) = sin(1), giving left-hand limit = sin(1).
Since sin(1) ≠ 0, the left-hand and right-hand limits are unequal, so the limit does not exist — which is none of the values listed (1, 0, or -1).
[1985]