Exercise 6, § 2

Show that on the interval $[ -1, +1 ]$ the function $|x|$ is the uniform of limit of polynomials, by remarking that $|x| = (1 - (1 - x^2))^{1/2}$ and using the binomial series. Deduce another proof of the Weierstrass th. from this (cf. II, p. 83, exerc. 20).