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## Homework Statement

Let f: R-->R be continuous. For δ>0, define g: R-->R by:

g(x) = (1/2δ) ∫ (from x-δ to x+δ) f

Show:

a) g is continuously differentiable

b) If f is uniformly continuous, then, for every ε>0, there exists a δ1>0 such that sup{∣f(x) - g(x)∣; x∈R} < ε for 0<δ≤δ1

## The Attempt at a Solution

Please help me, im confused

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