Jatkuvuus
Author: Simo K. Kivelä
Date: 3.11.2009

f_3(x) = x^(1 / 3)
ε = 0.53 (slider from 0.01 to 1, step 0.01)
δ = 0.341 (slider from 0.0010 to 1, step 0.0010)
a = 0
f_1(x) = x^(2) + 2 * x + 1
f: f_1
P: (a, f(a))
testvals: {-1, -0.99, -0.98, -0.97, -0.96, -0.95, -0.94, -0.93, -0.92, -0.91, -0.9, -0.89, -0.88, -0.87, -0.86, -0.85, -0.84, -0.83, -0.82, -0.81, -0.8, -0.79, -0.78, -0.77, -0.76, -0.75, -0.74, -0.73, -0.72, -0.71, -0.7, -0.69, -0.68, -0.67, -0.66, -0.65, -0.64, -0.63, -0.62, -0.61, -0.6, -0.59, -0.58, -0.57, -0.56, -0.55, -0.54, -0.53, -0.52, -0.51, -0.5, -0.49, -0.48, -0.47, -0.46, -0.45, -0.44, -0.43, -0.42, -0.41, -0.4, -0.39, -0.38, -0.37, -0.36, -0.35, -0.34, -0.33, -0.32, -0.31, -0.3, -0.29, -0.28, -0.27, -0.26, -0.25, -0.24, -0.23, -0.22, -0.21, -0.2, -0.19, -0.18, -0.17, -0.16, -0.15, -0.14, -0.13, -0.12, -0.11, -0.1, -0.09, -0.08, -0.07, -0.06, -0.05, -0.04, -0.03, -0.02, -0.01, 0, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1, 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2, 0.21, 0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3, 0.31, 0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4, 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6, 0.61, 0.62, 0.63, 0.64, 0.65, 0.66, 0.67, 0.68, 0.69, 0.7, 0.71, 0.72, 0.73, 0.74, 0.75, 0.76, 0.77, 0.78, 0.79, 0.8, 0.81, 0.82, 0.83, 0.84, 0.85, 0.86, 0.87, 0.88, 0.89, 0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99, 1}
e1 = Line((a, f(a) - ε), (a + 1, f(a) - ε))
e2 = Line((a, f(a) + ε), (a + 1, f(a) + ε))
d1 = Line((a - δ, f(a)), (a - δ, f(a) + 1))
d2 = Line((a + δ, f(a)), (a + δ, f(a) + 1))
test1 = Min(f(a) + ε - f(a + δ * testvals))
test2 = Min(f(a + δ * testvals) - f(a) + ε)
test: (test1 > 0) ∧ (test2 > 0)
K = (3.4392592592592592, 1.8407407407407408)
c = Circle(K, 0.2)
f_5 = If(x ≠ 0, sin(1 / x) / 2, 0)
f_4 = If(x < 0, (1 + x) / 2, 1 - x^(2))
f_2(x) = sin(2 * x)