This shows the graph of a certain sequence of functions over the interval [0,1]; it shows the graph of *f*_{n}(*x*)= *nx* *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 the graph of *f*_{n} is not close to zero over the entire interval [0,1]. (Move *x* back and forth to see this: the maximum of the function over [0,1] is *e*^{-1} = 0.368 for all *n*.) So this sequence of functions converges pointwise to 0 but not uniformly.