Piecewise Function Continuity and Differentiability
Let g be the function defined by g(x) = { x^2 sin(1/x) if x ≠ 0; 0 if x = 0 }. Which of the following statements is true about g at x = 0?
A
g is both continuous and differentiable at x = 0
B
g is continuous but not differentiable at x = 0
C
g is differentiable but not continuous at x = 0
D
g is neither continuous nor differentiable at x = 0
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