Graphical Limits Quiz

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2016-08-25 02:56

This example demonstrates visually understanding and practicing the concept of limits through graphical methods. Core math concepts include limits, function graphs, random experiments, histograms, and distributions. It uses GeoGebra commands and objects like Random (random number generation), If (conditional statements), Polynomial (polynomial functions), Textfield (text input), and Polygon (polygon drawing). Suitable for high school and above students learning calculus to assist in understanding and mastering limit calculations.

GeoGebra Commands & Parameters

Random(-10, 10) → x_A
Random(1, 10) → type
Random(-10, 10) → seed_B
If(seed_B ≟ x_A, (-x_A), seed_B) → x_B
If(type ≤ 3, x_A, If[type ≥ 8, x_B, Random[-5, 5]]) → break
If((type > 1) ∧ (type < 9), break, Random[-10, 10]) → x_C
Polynomial({(x_A, Random[-5, 5]), (x_B, Random[-3, 8]), (If[x_C ≟ x_A ∨ x_C ≟ x_B, -21, x_C], Random[-10, 10]), (Random[10, 20], Random[10, 20])}) → f
Polynomial({(x_A, Random[-2, 10]), (x_B, Random[-6, 3]), (If[x_C ≟ x_A ∨ x_C ≟ x_B, 21, x_C], Random[-10, 10]), (Random[-20, -11], Random[-20, 20]), (Random[11, 20], Random[-20, 20])}) → g
Random(0, 1) → left
If(x_A < break, Limit[f, x_A], If[x_A > break, Limit[g, x_A], If[f(x_A) ≟ g(x_A), f(x_A), -1000]]) → lim_A
If(type > 5, x_A, If[type < 5, x_B, Random[-5, 5]]) → holeX
If(x_B < break, Limit[f, x_B], If[x_B > break, Limit[g, x_B], If[f(x_B) ≟ g(x_B), f(x_B), -1000]]) → lim_B
Textfield(guessA) → guessABox
Textfield(guessB) → guessBBox
Random(0, 1) → right
If(x_C ≟ break, If[right ≟ 0, f(x_C), g(x_C)], If[x_C < break, f(x_C), g(x_C)]) → lim_C
Textfield(guessC) → guessCBox
Polygon((-12, -12), (-12, 12), (12, 12), (12, -12)) → poly1, a, b, c, d
Polygon((-12, -12), (-12, 12), (12, 12), (12, -12)) → poly2, e, i, j, k