Sequence of functions




This interactive page is intended to demonstrate the theorem that a sequence of functions that converge under the supremum metric will also converge under the integral metric and also converge pointwise.

The slider for \(n\) selects which \(f_n(x)\) is shown and the slider for \(x\) selects the value of \(x\) that is shown for illustrating pointwise convergence


\(f_n(x)=\frac{-x^4 + 7x^3 - (15 + 1 / n) x^2 + (11 + 1 / n) x + 4}{ n}\) for \(0\leq x\leq 3.5\).

Camilla Jordan, 15 October 2013, Created with GeoGebra