Summer 2021 - Fall 2023 New Stuff
Backstory webpage
Before Precalc
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line
-- line segment by dragging & by coordinates, midpoint, distance formula, point-slope equation, perpendicular, parallel lines
-- slide points A and B and generate equation of the line in 4 forms.
-- computes slopes and writes lines by sliding and by parameters
1 - drag segment endpoints to compute midpoint and distance
2 - show how the distance formula computes
3 - find a perpendicular w/input coordinates
4 - find parallel w/input coordinates
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2graphs.gsp
-- 1,2 graphed functions, piece-wise, composite ready to edit, link to "coordinate" and more history, table of f(x) gps files
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make.hexagon.gsp -- construct a hexagon, and also consider other polygons w/a look towards pi
Functions, Lines, Circles
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Cartesian -- definition and analytic history web page
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ssong.gsp -- slope from history, to sound, to words & numbers, through examples, to computation
0 - toc, history
1 - only 1 function
2 - parabola w/tangent line
3 - cubic w/tangent line
4 - polynomial
5 - rational
6 - compute slope drag 2 points
7 - dy/dx by definition
8 - m= given A, B
9 - 3 points define a parabola
10 - notes on 3 points define a parabola
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circle.tangent.normal.gsp
1 drag center & radius 2 create equation
2 enter h, k, r
3 perpendicul w/input coordinates
4 slide tangent then compute & write
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circleFormula.gsp --
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inverse.gsp
0 - vertical, horizontal line tests
1 - square root fx
2 - any function
3 - sqrt fx by parameters
4 - restricted domain on inverse
5 - arcsine
6 - arctangent
7 - f and inverse
8 - f, inverse, tangents --
Polynomial and Rational Functions
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compositeFX.gsp --
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parabola.gsp --
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compositeFx.poly.ratl.gsp
0 - graph of 1 function
1 - graphs of 2 functions
2 - composite of 4 functions
3 - polynomial. links to polynomial, dilations gif, quatratic.htm, equation, discriminant
4 - rational, rational function features & how to find them
5 - end behavior, battle of (Ax^m)/(Bx^n)
Right Triangle & Trig
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standardPosition.gsp
1 standard position angle central angle, negative & positive angle measures
2 angles coterminal?
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radianSector.gsp
1 intro angles degrees radians
2 radian questions
3 arc length angular speed sector area
4 sector and area
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veronica.gsp
1 - 1 standard position angle
2 - angles coterminal?
3 - 1 veronica angles -- trig fx of angles is 4 quadrants
4 - 2 veronica angles
5 - extra 2 veronica angles
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elevation.gsp - angle of elevation, depression, ladders w/h(x), y(x), and h(y), x(y), and h as variable, and h s a constant
Calculus Limits
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limit -- limit by epsilon-delta, by dragging x, by approach from L & R, by table
0 -The Modern Evolution of Limit and Its Symbols
1 - approach by dragging x
2 - by above & below x
3 - table of x, f(x), f'(x), f''(x) w/tangent line
4 - limit, as x goes to infinity, (Ax^m)/(Bx^n) battle pix, emd behavior
5 - limit as h goes to 0, derivative by limit of difference quotient
6 - by solpe of secant
7 - webpage sample epsilon-delta
8 - simple sample limit questions
9 - by epsilon-delta
- 10 - Squeeze to take a limit, link to proof Dx(sin(x) = cos(x)
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limh4Dx.gsp
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limitWquestions.gsp
Derivatives
Derivatives Web Page
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3
0 - resources including: derivative definition, calc cheat sheet,
link to derivative calculator, link to integration calculator, derivative connect-the-dots,
integration connecet-the-dots
1 - f'(x), tan line, TRACE f'(x), table
2 - Leibnitz, Newton pix
3 - limit as h goes to 0
4 - no table x, f(x), f'(x), f''(x), tangent line included
5 - build table x, f(x), f'(x), f''(x)
6 - hand-plot sums
7 - extra hand-plot
8 - auitomatic 2 fx plot
9 secant images, link to wikipedia
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Mean.Rolle.f'(x).f''(x).gsp
0 - by secant & lim as h --> 0 of DQ
1 - fx w/tangent line
2 - just c on interval
3 - tan line f(x), f'(x), f''(x)
4 - f, f', TRACE, table
5 - sine emoji, w/tan & trace, f', f''
6 - fx tan & trace emoji, f f', f''
7 - Mean Value Theorem. slide [a,b]
8 - Roll's Theorem, slide [a, b]
9 - derivative tests, f, f', f'', emoji
10 - s(t), s'(t), s''(t), RED
11 - no table x, fx, f'x, f''x
12 - extra Rolle's
13 - x,f,f',f'',RIGHT&LEFT
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tracef.f1.f2.f3.f4.gsp
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DerAnyFx.gps -- Derivative of Any Function
* One may trace the function and see coordinates displayed. * One may edit the function.
* One may graph the approximate derivative function. 1 - f(x) w/tangent line
2 - f(x) & TRACE 3 - any f(x): x, f(x), f'(x), f''(x)
4 - sin(x): x, f(x), f'(x), f''(x)
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tracef.f1.f2.f3.f4.gsp
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derivativeTests.gsp
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DERlnx.gsp --
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for related rates, use elevation.gsp - angle of elevation, depression, ladders w/h(x), y(x), and h(y), x(y), and h as variable, and h s a constant
Reimann Sums & Antiderivatives
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Intro2AntiDerivative.gsp
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ReimannSums.gsp -- partitions, boxes, area by sum, antiderivative by dots
Reimann Boxes & Sums, and Integration Teacher's Manual contains:
0 - toc
1a - background limit by approach
1b - LIMIT by definition, secant
1c - partition
1d - 1st page notes
1e - 2nd page notes
2 - PARTITION & SUMS 4 boxes
3a - REIMANN & SUMS
3b - subscript x1 start
4 - n=8 RLM
5 - Hump areas
6 - area f(x)- g(x), input [a,b] in the boxes for a and b
6b - probability distribution
7 - sum to integral
8 - INTEGRATION only 1st plus c
8a - building the points (xi, sumi)
8b - Notes green dots integration
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JUSTdots.gsp -- Plots points on an antiderivative, no support pages
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Justderivatives.gsp -- derivatives by definition, by tangent line, by traces of f', f'', f''', f''' (ideal for the trig cycle and for y=ex)
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JUSTdotsWreview.gsp -- Plots points on an antiderivative, includes some support pages
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