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CBSE Class 12 Mathematics 2026 Main Paper 65/3/2 · Q181 Markspiecewise_continuity

CBSE Class 12 Mathematics 2026 Main Paper 65/3/2 · Question 18 (Continuity And Differentiability)

Find k for continuity of f(x)=x² sin(1/x) for x≠0 and f(0)=k(0+1).

(A) 1/4
(B) 2
(C) 1/2
(D) 0

✅ Step-by-Step Solution

Final Answer: 0

The oscillating term has absolute value at most x² and tends to zero. Thus f(0)=k must be zero.

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