JEE Advanced Mathematics question
Let denote the greatest integer less than or equal to . Now is defined as below:
g(x)=
where . Then
- (A) is continuous and differentiable at when Correct
- (B) is continuous and differentiable at when
- (C) is continuous but not differentiable at when
- (D) is continuous but differentiable at when
Answer: (A)
Solution
For , : . Let .
- : , so , and . Then on , and . So on : continuous and differentiable at (with
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Question ID VK-109345