Limits

This worksheet can be used to help visualize the formal definition of limit.  THe function, g(x), can be changed by clicking on it.

L = Point(yAxis)
ε = 0.3 (slider from 0 to 1, step 0.01)
B: (0, y(L) - ε)
C: (0, y(L) + ε)
c_1 = OrthogonalLine(L, yAxis)
g(x) = (x^(3) - x) / 10
c = Point(xAxis)
h = OrthogonalLine(c, xAxis)
δ = 0.3 (slider from 0 to 2, step 0.01)
G: (x(c) + δ, 0)
H: (x(c) - δ, 0)
i = OrthogonalLine(H, xAxis)
j = OrthogonalLine(G, xAxis)
poly1, d, e, f, k = Polygon((-100, y(L) - ε), (-100, y(L) + ε), (100, y(L) + ε), (100, y(L) - ε))
poly2, a, b, l, m = Polygon((x(c) - δ, -100), (x(c) + δ, -100), (x(c) + δ, 100), (x(c) - δ, 100))