
LIMITS + CONTINUITY
Explore the ε, ∂ definition of limits
and the definition of continuity.
Evaluate the limits (full, lefthand or righthand) of any
function (including piecewise defined) as x →a or as x→±∞ 


MACLAURIN & TAYLOR SERIES
Enter any f(x). Overlay a Maclaurin or
Taylor Series polynomial of degree n & use it to approximate
the value of f(x) at any point t. Vertical gray bands show
where the power series is within a chosen tolerance to f(x).
As n increases, the band widens.



OPTIMIZATION
Interact with various classic applications to
find the most, lerasdy, cheapest, fastest, etc.
Graphed data includes tangent line & derivative analysis


RELATED RATES
A click of a button advances time to commence the
action to these classic problems.
Other buttons reveal the values
and graphs of the rates.


VOLUMES ON A BASE
Visualize these shapes one step at a time. Start
by rotating the xyplane to horizontal.
View a few stationary
slices, then a sweeping slice, and finally, an accumulating slice.
Rotate the solid any time for other viewing angles. Choose from an
assortment of bases and crosssections.

VOLUMES BY REVOLUTION
These animations cover both the disk/washer
technique and the cylindrical shell technique.
Develop the process
by first revolving one lone rectangle. Next, revolve several
rectangles in a region and stack or nest the results.
Finally,
revolve any desired region (bounded by 1 or 2 functions of choice)
on an interval of choice, about any horizontal or vertical axis.

