If f is a differentiable function satisfying = 0 for all n ≥ 1, n ∈ I , then

Mathematics · JEE Advanced · NTA ExamsLimit, Continuity and Differentiability

If f is a differentiable function satisfying = 0 for all n ≥ 1, nI, then
  1. f′(0) = 0 = f (0)
  2. |f (x)| ≤ 1, x ∈(0, 1)
  3. f (x) = 0, x ∈(0, 1]
  4. f (0) = 0 but f′(0) not necessarily zero

Answer

(A) f ′ (0) = 0 = f (0)

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