Continuity and Differentiability · Class 12 · CBSE · Science Mathematics
Define f(x) = (1 − cos x)/x² for x ≠ 0 and f(0) = 1/2. What can be concluded about f at x = 0?
Practice question from Continuity and Differentiability (Class 12 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.
medium · MCQ · Q-9075FA
Define f(x) = (1 − cos x)/x² for x ≠ 0 and f(0) = 1/2. What can be concluded about f at x = 0?
- A.f is both continuous and differentiable at x = 0Correct answer
- B.f is continuous but not differentiable at x = 0
- C.f is differentiable but not continuous at x = 0
- D.f is neither continuous nor differentiable at x = 0
Solution
Using , f is continuous at 0. Also, as , so f is differentiable at 0.
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