# Derivative of a linear piecewise function

 On the left is a piecewise linear function. On the left is the derivative of that piecewise linear function. 1) In the left window, drag points A, B, C, D, and E to see how the derivative changes. 2) How is the graph formed? 3) Why are there open circles in the derivative? Should they be connected? Explain.

# Accumulating Penguins

In a math twitter discussion about calculus, the idea was brought up of penguins entering a room. [br][br]If this many entered each minute, how many penguins?

# The limit of a sequence

 The limit of the sequence ($a_n$) is $L$ if given any $\varepsilon>0$, there is an $N>$0 such that $|a_n-L|<\varepsilon$ for all $n\ge N$. The yellow band is $L±\varepsilon$ and the blue region correspons to those $n\ge N$. The green dots are within $\varepsilon$ of $L$ and the red dots and red x's are not. The limit is $L$ if for any given $\varepsilon$ you are able to move the blue region far enough to the right that there are no red x's. Note: To move the window, hold the shift key down while you click and drag. To zoom in or out, hold down the shift key and scroll the mouse.