Maths · Limits, continuity and differentiability
The set of all values of 'a' for which \) does not exist is \) denotes greatest
The set of all values of 'a' for which \( \lim _{x \rightarrow a}[x] \) does not exist is \( ([x] \) denotes greatest integer function)
- A. a is any integer
- B. a is a positive rational number
- C. a is a negative rational integer
- D. a is complex number
Step-by-step solution
The greatest integer function [x] is discontinuous at integer points. For any integer a, the left-hand limit as x→a- is a-1, and the right-hand limit as x→a+ is a, which are not equal, so the limit does not exist. For non-integer a, the function is continuous, so the limit exists. Therefore, the set of all a for which the limit does not exist is all integers.
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