Exercise 7(Continuityof Contraction Maps) Recall that a function fis a contraction map if there exists akin(0,1) with x,y??anxnrn0?ann+1xn+1??anxn=n0?(-1)nx2n|f(x)-f(y)| for all x,y. Prove that contraction maps are continuous.Exercise 8 Let ??anxnbe a power series with radius of convergence r, and assume that the ratio test worksfor computing this.Use the Ratio Test to prove that integrating term-by-term gives a power series with the same radius ofconverenge:n0?ann+1xn+1While the radius of convergence is the same for both series, show the behavior at the endpoints neednot be,by studying the example ??anxn=n0?(-1)nx2n.