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from manimlib.imports import *
class limitfin2(GraphScene):
CONFIG = {
"x_min" : -8,
"x_max" : 8,
"x_labeled_nums" : list(range(-8, 10, 3)),
"x_axis_width" : FRAME_WIDTH - LARGE_BUFF,
"y_min" : -4,
"y_max" : 4,
"y_labeled_nums" : None,#list(range(3,,)),
"y_axis_height" : FRAME_HEIGHT+2*LARGE_BUFF,
"graph_origin" : DOWN,
"graph_color" : BLUE,
"x_axis_width":20,
"y_axis_height":10,
}
def construct(self):
self.setup_axes()
XTD = 10/(8 - (-8))
YTD = 10/(4 - (-4))
graph1 = self.get_graph(lambda x: -(-(0.25*x**2)-1), x_min = self.x_min, x_max = -0.1)
graph2 = self.get_graph(lambda x: ((0.25*x**2)+2), x_min = 0.1, x_max = self.x_max, color = self.graph_color)
dot1 = Circle(radius = 0.1).move_to(self.graph_origin+1*UP*YTD)
dot2 = Circle(radius = 0.1).move_to(self.graph_origin+2*UP*YTD)
text1 = TexMobject(r"\text{It doesn't matter how small }", r"\delta",r"\text{ gets, }" r"\epsilon" r"\text{ does not tend to zero}").move_to(self.graph_origin+2*DOWN)
self.play(ShowCreation(graph1), ShowCreation(graph2), ShowCreation(text1), FadeIn(dot1), FadeIn(dot2))
line1 = DashedVMobject(Line(self.graph_origin+1*DOWN*YTD+1*LEFT*XTD, self.graph_origin+4*UP*YTD+1*LEFT*XTD), num_dashes = 50).set_color(PINK)
line2 = DashedVMobject(Line(self.graph_origin+1*DOWN*YTD+1*RIGHT*XTD, self.graph_origin+4*UP*YTD+1*RIGHT*XTD), num_dashes = 50).set_color(PINK)
line3 = DashedVMobject(Line(self.graph_origin+1.5*UP*YTD+5*LEFT*XTD, self.graph_origin+1.5*UP*YTD+4*RIGHT*XTD), num_dashes = 50).set_color(GOLD)
line4 = DashedVMobject(Line(self.graph_origin+0.5*UP*YTD+5*LEFT*XTD, self.graph_origin+0.5*UP*YTD+4*RIGHT*XTD), num_dashes = 50).set_color(GOLD)
line5 = DashedVMobject(Line(self.graph_origin+2.5*UP*YTD+5*LEFT*XTD, self.graph_origin+2.5*UP*YTD+4*RIGHT*XTD), num_dashes = 50).set_color(GOLD)
self.play(ShowCreation(line1), ShowCreation(line2))
vec1 = Line(self.graph_origin, self.graph_origin+1*RIGHT*XTD)
vec2 = Line(self.graph_origin, self.graph_origin+1*LEFT*XTD)
vec5 = Line(self.graph_origin+2.5*UP*YTD+4*RIGHT*XTD, self.graph_origin+1.5*UP*YTD+4*RIGHT*XTD)
vec6 = Line(self.graph_origin+0.5*UP*YTD+4*RIGHT*XTD, self.graph_origin+1.5*UP*YTD+4*RIGHT*XTD)
brace1 = Brace(vec1, DOWN)
brace2 = Brace(vec2, DOWN)
br1text = brace1.get_text(r"$\delta$").next_to(brace1, DOWN)
br2text = brace2.get_text(r"$\delta$").next_to(brace2, DOWN)
brace5 = Brace(vec5, RIGHT)
brace6 = Brace(vec6, RIGHT)
br5text = brace5.get_text(r"$\epsilon$").next_to(brace5, RIGHT)
br6text = brace6.get_text(r"$\epsilon$").next_to(brace6, RIGHT)
self.wait(3)
self.play(ShowCreation(brace1), ShowCreation(brace2), ShowCreation(br1text), ShowCreation(br2text))
self.wait(3)
self.play(ShowCreation(line3), ShowCreation(line4), ShowCreation(line5), ShowCreation(brace5), ShowCreation(brace6), ShowCreation(br5text), ShowCreation(br6text))
vec3 = Line(self.graph_origin, self.graph_origin+0.1*RIGHT*XTD)
vec4 = Line(self.graph_origin, self.graph_origin+0.11*LEFT*XTD)
brace3 = Brace(vec3, DOWN)
brace4 = Brace(vec4, DOWN)
vec7 = Line(self.graph_origin+2.1*UP*YTD+4*RIGHT*XTD, self.graph_origin+1.5*UP*YTD+4*RIGHT*XTD)
vec8 = Line(self.graph_origin+0.9*UP*YTD+4*RIGHT*XTD, self.graph_origin+1.5*UP*YTD+4*RIGHT*XTD)
brace7 = Brace(vec7, RIGHT)
brace8 = Brace(vec8, RIGHT)
self.play(Transform(brace1, brace3), Transform(brace2, brace4), ApplyMethod(line2.shift, 0.8*LEFT*XTD),
ApplyMethod(line1.shift, 0.8*RIGHT*XTD), ApplyMethod(br1text.scale, 0.3), ApplyMethod(br2text.scale, 0.3),
Transform(brace5, brace7), Transform(brace6, brace8), ApplyMethod(line4.shift, 0.8*UP*XTD),
ApplyMethod(line5.shift, 0.8*DOWN*XTD))
self.play(FadeOut(brace3), FadeOut(brace4), FadeOut(brace1), FadeOut(brace2))
self.play(ApplyMethod(line2.shift, 0.8*RIGHT*XTD), ApplyMethod(line1.shift, 0.8*LEFT*XTD), ApplyMethod(br1text.scale, 10/3), ApplyMethod(br2text.scale, 10/3))
for i in range(0,3):
self.play(ApplyMethod(line2.shift, 0.8*LEFT*XTD), ApplyMethod(line1.shift, 0.8*RIGHT*XTD), ApplyMethod(br1text.scale, 0.3), ApplyMethod(br2text.scale, 0.3), run_time = 0.5)
self.play(ApplyMethod(line2.shift, 0.8*RIGHT*XTD), ApplyMethod(line1.shift, 0.8*LEFT*XTD), ApplyMethod(br1text.scale, 10/3), ApplyMethod(br2text.scale, 10/3), run_time = 0.5)
self.play(ApplyMethod(line2.shift, 0.8*LEFT*XTD), ApplyMethod(line1.shift, 0.8*RIGHT*XTD), ApplyMethod(br1text.scale, 0.3), ApplyMethod(br2text.scale, 0.3), run_time = 0.5)
self.wait(5)
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