This shows the graph of a certain sequence of functions over the interval [0,1]; it shows the graph of *f*_{n}(*x*)= *x* *e*^{-nx} for the indicated value of *n*.

**What to do:**

Change the value of *x* by moving the vertical grey rectangle to the left or right (by clicking and dragging with the mouse).

Increase *n* or reset *n* to 1 by clicking on the buttons on the lower left.

Notice that as you increase *n*, the value of *f*_{n}(*x*) for the current value of *x* eventually goes to 0. But also notice that the graph of *f*_{n} gets close to zero over the entire interval [0,1], as *n* increases (move *x* back and forth to see this). So this sequence of functions converges uniformly to 0 on [0,1].