Let f be acontinuous functionon open interval I.

Let h>0 and a<b so that: (a-h,b+h) c I.

Now we choose d: 0 < d< h

and now for every x in(a,b) we define the following function:

G(x) = 1/2d * {int(-d --> d) f(x+t)dt}

Prove:

1. G is differentiable functions whose derivative is continuous.

2. lim(d-->0+) G(x) = f(x)

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