GATE CE 2023 Set 1 — Question 48
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Engineering Mathematics → Calculus → Differentiability
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Question
For the function , which of the following statements is/are TRUE?
Correct answer
(A) The function is continuous at all x
Solution
(A) is continuous everywhere and is continuous everywhere. Their product is continuous at all . TRUE.
(B) is not differentiable at (where ). At these points, the left-hand and right-hand derivatives of differ. FALSE.
(C) . The function is not periodic. FALSE.
(D) As , . Since oscillates between 0 and 1, is not bounded. FALSE.
(B) is not differentiable at (where ). At these points, the left-hand and right-hand derivatives of differ. FALSE.
(C) . The function is not periodic. FALSE.
(D) As , . Since oscillates between 0 and 1, is not bounded. FALSE.
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