函數的極限
Author: 藍邦偉  老師

$ (a,f(a)) $

$ x=a $

$ f(a) $

$ (a+δ,f(a+δ)) $

$ (a-δ,f(a-δ)) $

$ f(a)+\varepsilon$

$ f(a-\varepsilon)$

$ f(a+δ) $

$ f(a-δ) $

$ x=a+δ $

$ x=a-δ $

$ 函數的極限 $

$ O $

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
Q_2: 0.8 * Corner[1] + 0.2 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
ε = 2 (slider from 0.1 to 2, step 0.1)
δ = 1.5 (slider from 0.1 to 2, step 0.1)
A = (-1.4954683805894176, -1.8871496490859345)
B = (1.655716727839901, 2.218940037655296)
C = (4.9023922941004106, 4.472514842471414)
D = (7.461536563976342, 3.1547465244009723)
f = Polynomial({A, B, C, D})
n = 0 (slider from 0 to 3, step 1)
P = Point(f)
P_{x}: (x(P), 0)
P_{y}: (0, y(P))
a = Segment(P, P_{x})
b = Segment(P, P_{y})
P_{x+}: P_{x} + (δ, 0)
P_{x-}: P_{x} - (δ, 0)
P_{y+}: P_{y} + (0, ε)
P_{y-}: P_{y} - (0, ε)
P_{-}: (x(P) - δ, f(x(P) - δ))
P_{+}: (x(P) + δ, f(x(P) + δ))
Q_{+}: (0, y(P_{+}))
Q_{-}: (0, y(P_{-}))
c = Segment(Q_{+}, P_{+})
d = Segment(P_{+}, P_{x+})
e = Segment(P_{-}, P_{x-})
g = Segment(P_{-}, Q_{-})
poly2, p_{+}, q_{+}, q_{-}, p_{-}, p_{x-}, p_{x+} = Polygon(P_{+}, Q_{+}, Q_{-}, P_{-}, P_{x-}, P_{x+})
h = Segment(P_{y+}, P_{y-})