NDA 2025 · PYQ · Limits / Piecewise functions · easy
Let f(x) = { x³, x² < 1; x², x² ≥ 1 }. What is lim(x→0) f'(x) equal to?
- A.2
- B.1
- C.0✓ Correct
- D.Limit does not exist
For x² < 1 (i.e., −1 < x < 1), f(x) = x³, so f'(x) = 3x². As x → 0, f'(x) = 3x² → 0. Hence the limit is 0.
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