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from manimlib.imports import*
import math
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(-8, 8, 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)
self.setup_axes(animate=True)
lnx=self.get_graph(lambda x:math.log2(x),color=RED,x_min=0.01,x_max=8)
equation=self.get_graph(lambda x:math.log2(2)+(x-2)/2-((x-2)**2)/8+((x-2)**3)/24-((x-2)**4)/64+((x-2)**5)/160-((x-2)**6)/384,color=BLUE)
terms=[TextMobject("$T_{n}:=$"),TextMobject("$ln(2)$"),TextMobject("$+\\frac { x-2 }{ 2 } $"),TextMobject("$-\\frac { (x-2)^{2} }{ 8 }$"),TextMobject("+..")]
for obj in terms:
obj.scale(0.5)
terms[0].shift(3*UP+3*RIGHT)
terms[1].next_to(terms[0],buff=0.1)
terms[2].next_to(terms[1],buff=0.1)
terms[3].next_to(terms[2],buff=0.1)
terms[4].next_to(terms[3],buff=0.1)
self.play(ShowCreation(lnx))
self.wait(1)
self.play(FadeIn(equation),FadeIn(terms[0]),FadeIn(terms[1]),FadeIn(terms[2]),FadeIn(terms[3]),FadeIn(terms[4]))
self.wait(1)
bottomText1=TextMobject("$R_{n}(x)=\\frac { d }{ dx } ($","area bounded","$)$")
bottomText1.set_color_by_tex_to_color_map({"area bounded":ORANGE})
#bottomText2.set_color_by_tex_to_color_map({"area bounded":BLUE})
arrow=TextMobject("$\downarrow$")
arrow.scale(2.5)
arrow.shift(ORIGIN+x_each_unit*RIGHT*9.5+UP*y_each_unit)
increasingText=TextMobject("Increases!")
increasingText.set_color(GREEN)
followupText=TextMobject("as n increase!")
followupText.scale(0.3)
followupText.shift(ORIGIN+x_each_unit*11*RIGHT+UP*y_each_unit*1.1)
increasingText.shift(ORIGIN+x_each_unit*11*RIGHT+UP*y_each_unit*1.6)
increasingText.scale(0.4)
bottomText1.scale(0.5)
#bottomText2.scale(0.5)
#bottomText3.scale(0.5)
bottomText1.shift(3.5*LEFT+2*DOWN)
#bottomText2.shift(3.5*LEFT+2.4*DOWN)
#bottomText3.shift(3.5*LEFT+2.8*DOWN)
dline=DashedLine(start=ORIGIN+8*y_each_unit*UP,end=ORIGIN+8*y_each_unit*DOWN)
dline.shift(ORIGIN+x_each_unit*4*RIGHT)
area1=self.get_riemann_rectangles(lnx,x_max=8,x_min=4,dx=0.01,start_color=BLUE,end_color=RED,stroke_width=0,fill_opacity=0.8)
area2=self.get_riemann_rectangles(equation,x_max=5.2,x_min=4,dx=0.025,start_color=BLACK,end_color=BLACK,stroke_width=0,fill_opacity=1)
self.play(Write(dline))
self.wait(0.5)
self.play(ShowCreation(area1),ShowCreation(area2),Write(bottomText1))
# self.play(Write(bottomText2))
# self.play(FadeIn(bottomText3))
self.play(Write(arrow))
self.wait(0.7)
self.play(Write(increasingText))
self.play(FadeIn(followupText))
self.wait(2)
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