Q73.If f(x) = [x] −[ x4 ], x ∈R, where [x] denotes the greatest integer function, then: (1) x→4+f(x)lim exists but x→4−f(x)lim does not exist (2) f is continuous at x = 4 (3) x→4−f(x)lim exists but x→4+f(x)lim does not exist (4) Both x→4−f(x)lim and x→4+f(x)lim exist but are not equal
What This Question Tests
The problem tests the understanding of limits and continuity for functions involving the greatest integer function. It requires evaluating the left-hand and right-hand limits at `x=4` and comparing them to check for existence and equality.
Concepts Tested
Formulas Used
[x] = n if n <= x < n+1
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📋 Question Details
- Chapter
- Limits & Continuity
- Topic
- Limits of greatest integer function
- Year
- 2019
- Shift
- 09 Apr Shift 2
- Q Number
- Q73
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 5: Continuity and Differentiability
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