EDB — 1V9

Exercises

1. [1V9] Note:exercise 1, June 7th 2010.

   Prove that there exists one and only one continuous function \(f\) on the interval \([-1, 1]\) such that

   \[ f(x)=1+\frac{x}{2}f\big(x^ 2\big)\quad ∀ x∈ [-1,1]\quad . \]

   Prove that \(f\) is representable as a power series centered at zero; and that the radius of convergence is one.

   Solution 1

   [1VB]↺↻