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OPTIMIZATION
Interact with various classic applications to
find the most, lerasdy, cheapest, fastest, etc.
Graphed data includes tangent line & derivative analysis
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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.
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VOLUMES ON A BASE
Visualize these shapes one step at a time. Start
by rotating the xy-plane 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 cross-sections.
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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.
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SLOPE FIELDS + EULER'S METHOD
To introduce what a slope field is, use the graph
of f ’ to see its values controlling a gliding dynamic “slope
column”.
Snapshots of this column are the
slope field. A tangent segment “pilots” the field to draw f.
Once understood, a different animation allows any differential
equation to be entered and generates the slope field.
Manually follow the field to draw f or use Euler’s Method (includes
explanation of E.M. and numerical table of data). Easily adjustable. |
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LIMITS
Explore the ε, ∂ definition of limits.
Evaluate the limits (full, left-hand or right-hand) of any
function (including piece-wise defined) as x →a or as x→±∞ |
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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.
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