f(x)= cases [x^2]-[-x^2], & x 3 k, & x=3 cases is continuous at x = 3, then k = where [ ] is greatest integer function

MHT CET 2025 Mathematics question

is continuous at x = 3, then k = where is greatest integer function

(A)0
(B)1
(C)-1Correct
(D)3

Answer: (C)

Solution

For continuity at we need , so we must find the limit of the greatest-integer expression near , where is close to 9 but not an integer. For a non-integer we have the identity (for example ). So the expression that has the same limit from both

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Question ID VK-101241