## 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