Exercises
[14Y] Let \(x_ n,y_ n\) be strictly positive real sequences with limit zero; there is a continuous and monotonic function \(f:[0,β)β [0,β)\) such that \(f(0)=0\) and \(β x{\gt}0, f(x){\gt}0\), and such that \(β n, f(x_ n){\lt}y_ n\) (hence \(\lim _{xβ 0+}f(x)=0\)).
Solution 1