Basic Analysis I — Real Analysis · Problem 4.1.6

The Derivative — Jiri Lebl

Mathematics — Real Analysis · differentiability-sine-at-zero

Problem

Assume the inequality ∣x−sin⁡(x)∣≤x2|x - \sin(x)| \leq x^2. Prove that sin⁡\sin is differentiable at 00, and find the derivative at 00.

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