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from manimlib.imports import*
import math
class intro(Scene):
def construct(self):
introText1=TextMobject("Let's analyse")
introText2=TextMobject("for")
function_main=TextMobject("$\sum { { (-1) }^{ n }{ x }^{ 2n } }$")
function_main.set_color(GREEN)
introText1.scale(1.2)
introText1.shift(2*UP)
introText2.scale(0.7)
introText2.shift(UP)
function_main.scale(2)
function_main.shift(DOWN)
function_expan=TextMobject("$1-{ x }^{ 2 }+{ x }^{ 4 }-{ x }^{ 6 }+{ x }^{ 8 }+..$")
function_expan.set_color(RED)
function_expan.scale(1.2)
function_expan.shift(2*UP)
self.play(Write(introText1))
self.play(FadeIn(introText2))
self.wait(0.5)
self.play(Write(function_main))
self.wait(1)
self.play(FadeOut(introText1),FadeOut(introText2))
self.play(ApplyMethod(function_main.shift,3*UP))
self.wait(0.5)
self.play(ReplacementTransform(function_main,function_expan))
self.wait(1)
self.play(ApplyMethod(function_expan.scale,0.5))
function_expan.to_edge(UP+RIGHT)
self.play(ReplacementTransform(function_expan,function_expan))
self.wait(1)
class graphScene(GraphScene):
CONFIG = {
"x_min": -8,
"x_max": 8,
"y_min": -8,
"y_max": 8,
"graph_origin": ORIGIN,
"function_color": RED,
"axes_color": GREEN,
"x_axis_label": "$x$",
"y_axis_label": "$y$",
"exclude_zero_label": True,
"x_labeled_nums": range(-1, 2, 1),
"y_labeled_nums": range(0,2,1)
}
def construct(self):
x_each_unit = self.x_axis_width / (self.x_max - self.x_min)
y_each_unit = self.y_axis_height / (self.y_max - self.y_min)
function_expan=TextMobject("$1-{ x }^{ 2 }+{ x }^{ 4 }-{ x }^{ 6 }+{ x }^{ 8 }+..$")
function_expan.set_color(RED)
function_expan.scale(0.6)
function_expan.to_edge(UP+RIGHT)
self.add(function_expan)
self.setup_axes(animate=True)
eqText=[TextMobject("$1$"),TextMobject("$1-{ x }^{ 2 }$"),TextMobject("$1-{ x }^{ 2 }+{ x }^{ 4 }$"),TextMobject("$1-{ x }^{ 2 }+{ x }^{ 4 }-{ x }^{ 6 }$")]
for i in range(0,len(eqText)):
eqText[i].scale(0.6)
eqText[i].set_color(BLUE)
eqText[i].shift(ORIGIN+UP*2*y_each_unit+RIGHT*3.3*x_each_unit)
eqTextTerm=TextMobject("And so on..!")
eqTextTerm.set_color(BLUE)
eqTextTerm.scale(0.6)
eqTextTerm.shift(ORIGIN+UP*2*y_each_unit+3*RIGHT*x_each_unit)
equation1 = self.get_graph(lambda x : 1,color = RED,x_min = -8,x_max=8)
equation2 = self.get_graph(lambda x : 1-math.pow(x,2),color = RED,x_min = -1.7,x_max=1.7)
equation3 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4),color = RED,x_min = -1.6,x_max=1.6)
equation4 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6),color = RED,x_min = -1.45,x_max=1.45)
equation5 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6)+math.pow(x,8),color = RED,x_min = -1.35,x_max=1.35)
equation6 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6)+math.pow(x,8)-math.pow(x,10),color = RED,x_min = -1.3,x_max=1.3)
equation7 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6)+math.pow(x,8)-math.pow(x,10)+math.pow(x,12),color = RED,x_min = -1.25,x_max=1.25)
equation8 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6)+math.pow(x,8)-math.pow(x,10)+math.pow(x,12)-math.pow(x,14),color = RED,x_min = -1.2,x_max=1.2)
equation9 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6)+math.pow(x,8)-math.pow(x,10)+math.pow(x,12)-math.pow(x,14)+math.pow(x,16),color = RED,x_min = -1.15,x_max=1.15)
equation10 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6)+math.pow(x,8)-math.pow(x,10)+math.pow(x,12)-math.pow(x,14)+math.pow(x,16)-math.pow(x,18),color = RED,x_min = -1.15,x_max=1.15)
textBtwAnim1=TextMobject("Here the graph just","oscilates")
textBtwAnim1.set_color_by_tex_to_color_map({"oscilates":BLUE})
textBtwAnim2=TextMobject("after","the","point","(as we add higher order terms)")
textBtwAnim2.set_color_by_tex_to_color_map({"after":BLUE,"point":YELLOW})
textBtwAnim3=TextMobject("$x=1$")
textBtwAnim1.scale(0.4)
textBtwAnim2.scale(0.4)
textBtwAnim3.scale(1.2)
textBtwAnim1.shift(2.1*DOWN+4.3*RIGHT)
textBtwAnim2.shift(2.4*DOWN+4.1*RIGHT)
textBtwAnim3.shift(2.9*DOWN+4.3*RIGHT)
self.play(ShowCreation(equation1),run_time=0.8)
self.add(eqText[0])
self.wait(1)
self.play(ReplacementTransform(equation1,equation2),ReplacementTransform(eqText[0],eqText[1]))
self.wait(0.5)
self.play(ReplacementTransform(equation2,equation3),ReplacementTransform(eqText[1],eqText[2]))
self.wait(0.4)
self.play(ReplacementTransform(equation3,equation4),ReplacementTransform(eqText[2],eqText[3]))
self.wait(0.3)
self.play(FadeOut(eqText[3]))
self.play(FadeIn(eqTextTerm))
self.play(Write(textBtwAnim1),Write(textBtwAnim2))
self.play(FadeIn(textBtwAnim3))
self.play(ReplacementTransform(equation4,equation5))
self.wait(0.2)
self.play(ReplacementTransform(equation5,equation6))
self.wait(0.2)
self.play(ReplacementTransform(equation6,equation7))
self.wait(0.2)
self.play(ReplacementTransform(equation7,equation8))
self.wait(0.2)
self.play(ReplacementTransform(equation8,equation9))
self.wait(0.2)
self.play(ReplacementTransform(equation9,equation10))
self.wait(1)
self.play(FadeOut(textBtwAnim1),FadeOut(textBtwAnim2),FadeOut(textBtwAnim3),FadeOut(equation10),FadeOut(eqTextTerm))
self.wait(1)
convergeLine=Line(start=ORIGIN+x_each_unit*LEFT,end=ORIGIN+x_each_unit*RIGHT,color=WHITE)
divergeLineLeft=Line(start=ORIGIN+x_each_unit*LEFT,end=ORIGIN+x_each_unit*LEFT*8,color=RED)
divergeLineRight=Line(start=ORIGIN+x_each_unit*RIGHT,end=ORIGIN+x_each_unit*8*RIGHT,color=RED)
circle1=Circle(radius=0.01,color=PURPLE_E)
circle2=Circle(radius=0.01,color=PURPLE_E)
circle1.shift(ORIGIN+LEFT*x_each_unit)
circle2.shift(ORIGIN+RIGHT*x_each_unit)
convergeText=TextMobject("Converges")
divergeText1=TextMobject("Diverges")
divergeText2=TextMobject("Diverges")
convergeText.set_color(GREEN)
divergeText1.set_color(RED)
divergeText2.set_color(RED)
convergeText.scale(0.5)
divergeText1.scale(0.5)
divergeText2.scale(0.5)
convergeText.shift(1.6*UP)
divergeText1.shift(0.3*UP+1.5*LEFT)
divergeText2.shift(0.3*UP+1.5*RIGHT)
self.play(Write(divergeLineLeft),Write(divergeLineRight))
self.play(FadeIn(convergeLine))
self.wait(0.5)
self.play(FadeOut(self.axes))
self.play(Write(circle1),Write(circle2))
self.wait(0.5)
self.play(ApplyMethod(convergeLine.shift,1.3*UP),ApplyMethod(function_expan.shift,5*LEFT+DOWN))
self.play(FadeIn(convergeText),FadeIn(divergeText1),FadeIn(divergeText2))
self.wait(2)
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