Continuity and Differentiability

⭐ Important Questions

1. Check continuity of f(x) = {x² sin(1/x), x≠0; 0, x=0} at x=0.
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   limx→0 x² sin(1/x) = 0 (squeeze theorem, since -x² <= x² sin(1/x) continuous.
2. Find k if f(x) = {kx², x2} is continuous at x=2.
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   LHL = limx→2^- kx² = 4k\nRHL = limx→2^+ 3 = 3\nf(2) = 4k\nFor continuity: 4k = 3 => k = 3/4