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-rw-r--r--FSF-2020/calculus/intro-to-calculus/limit/Test1.py34
-rw-r--r--FSF-2020/calculus/intro-to-calculus/limit/Test2.py26
-rw-r--r--FSF-2020/calculus/intro-to-calculus/limit/limit1.py105
-rw-r--r--FSF-2020/calculus/intro-to-calculus/limit/limit3.py95
-rw-r--r--FSF-2020/calculus/intro-to-calculus/limit/limitdef.py73
5 files changed, 333 insertions, 0 deletions
diff --git a/FSF-2020/calculus/intro-to-calculus/limit/Test1.py b/FSF-2020/calculus/intro-to-calculus/limit/Test1.py
new file mode 100644
index 0000000..bd7d2a6
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/limit/Test1.py
@@ -0,0 +1,34 @@
+from manimlib.imports import *
+class Test1(GraphScene):
+ CONFIG = {
+ "y_max" : 5,
+ "y_min" : -5,
+ "x_max" : 5,
+ "x_min" : -5,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "axes_color" : BLUE,
+ "num_graph_anchor_points": 3000, #this is the number of points that graph manim
+ "graph_origin" : ORIGIN,
+ "x_labeled_nums": list(range(-5,6)),
+ "y_labeled_nums": list(range(-5,6)),
+ "x_axis_label":"$x$",
+ "y_axis_label":"${ f }_{ 1 }(x)$"
+ }
+ def construct(self):
+ self.setup_axes()
+ cir1 = Circle(radius = 0.1, color = BLUE)
+ graph_1 = self.get_graph(lambda x : x+2,
+ color = GREEN,
+ x_min = -5, # Domain 1
+ x_max = +1.9
+ )
+ graph_2 =self.get_graph(lambda x : x+2,
+ color = GREEN,
+ x_min = 2.1, # Domain 2
+ x_max = 5
+ )
+ cir1.move_to(np.array([1,2,0]))
+ self.play(ShowCreation(graph_1))
+ self.play(ShowCreation(cir1))
+ self.play(ShowCreation(graph_2))
diff --git a/FSF-2020/calculus/intro-to-calculus/limit/Test2.py b/FSF-2020/calculus/intro-to-calculus/limit/Test2.py
new file mode 100644
index 0000000..0efb565
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/limit/Test2.py
@@ -0,0 +1,26 @@
+from manimlib.imports import *
+class Test2(GraphScene):
+ CONFIG = {
+ "y_max" : 5,
+ "y_min" : -5,
+ "x_max" : 5,
+ "x_min" : -5,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "axes_color" : BLUE,
+ "num_graph_anchor_points": 3000, #this is the number of points that graph manim
+ "graph_origin" : ORIGIN,
+ "x_labeled_nums": list(range(-5,6)),
+ "y_labeled_nums": list(range(-5,6)),
+ "x_axis_label":"$x$",
+ "y_axis_label":"${ f }_{ 1 }(x)$"
+ }
+ def construct(self):
+ self.setup_axes()
+ graph_1 = self.get_graph(lambda x : x+2,
+ color = GREEN,
+ x_min = -5, # Domain 1
+ x_max = +5
+ )
+ self.play(ShowCreation(graph_1))
+ self.wait()
diff --git a/FSF-2020/calculus/intro-to-calculus/limit/limit1.py b/FSF-2020/calculus/intro-to-calculus/limit/limit1.py
new file mode 100644
index 0000000..fe5cb1e
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/limit/limit1.py
@@ -0,0 +1,105 @@
+from manimlib.imports import *
+class limit1(GraphScene,MovingCameraScene):
+ def setup(self):
+ GraphScene.setup(self)
+ MovingCameraScene.setup(self)
+ CONFIG = {
+ "y_max" : 1,
+ "y_min" : 0,
+ "x_max" : 1,
+ "x_min" : -1,
+ "y_tick_frequency" : 0.2,
+ "x_tick_frequency" : 0.2,
+ "axes_color" : WHITE,
+ "num_graph_anchor_points": 3000, #this is the number of points that graph manim
+ "graph_origin" : ORIGIN+3*DOWN,
+ "x_labeled_nums": list(range(-1,2)),
+ "y_labeled_nums": list(range(0,2)),
+ "x_axis_label":"$x$",
+ "y_axis_label":"$f(x)$",
+ "x_axis_width": 10,
+ "y_axis_height": 5,
+ }
+ def construct(self):
+ XTD = self.x_axis_width/(self.x_max - self.x_min)
+ YTD = self.y_axis_height/(self.y_max - self.y_min)
+
+ dot1 = SmallDot(np.array([0.025,-2.975,0]))
+ dot2 = SmallDot(np.array([-0.025,-2.975,0]))
+ sqr = Square(side_length = 15.0).move_to(np.array([0,-3,0]))
+ brline1 = DashedVMobject(Line(np.array([0.15,-3,0]), np.array([0.15,-2.85,0])))
+ brline2 = DashedVMobject(Line(np.array([0.025,-3,0]), np.array([0.025,-2.975,0])))
+ brline3 = DashedVMobject(Line(np.array([-0.15,-3,0]), np.array([-0.15,-2.85,0])))
+ brline4 = DashedVMobject(Line(np.array([-0.025,-3,0]), np.array([-0.025,-2.975,0])))
+ textdef = TextMobject("")
+ text003 = TextMobject("0.03").move_to(np.array([0.15,-3.05,0])).scale(0.1)
+ textazero1 = TexMobject(r"\approx 0").move_to(np.array([0.04,-3.05,0])).scale(0.1)
+ textazero2 = TexMobject(r"\approx 0").move_to(np.array([-0.04,-3.05,0])).scale(0.1)
+ textm003 = TextMobject("-0.03").move_to(np.array([-0.15,-3.05,0])).scale(0.1)
+ text2 = TextMobject("Let f(x) = |x|. We'll check neighbourhood of origin")
+ text3 = TextMobject("h has to be a very small number greater than 0").move_to(np.array([0,-3.3,0])).scale(0.2)
+ text4 = TextMobject("The point travels through range of neighbourhood").move_to(np.array([0,-3.3,0])).scale(0.19)
+ text5 = TextMobject("let h be equal to 0.03").move_to(np.array([0,-3.3,0])).scale(0.25)
+ text6 = TextMobject("Notice how the point never touches the origin").move_to(np.array([0,-3.3,0])).scale(0.2)
+ text7 = TextMobject("Green line shows the Right hand neighbourhood of origin").move_to(np.array([0,-3.3,0])).scale(0.17)
+ text8 = TextMobject("The point is approaching (0,0) for the values of x which are positive").move_to(np.array([0,-3.3,0])).scale(0.1)
+ text9 = TextMobject("Values of x are tending to 0 from positive side").move_to(np.array([0,-3.3,0])).scale(0.19)
+ text10 = TexMobject(r"\text {Notation for this is }",r"x\rightarrow { 0 }^{ + }").move_to(np.array([0,-3.3,0])).scale(0.25)
+ text11 = TextMobject("Similar case can be made for negative values of x").move_to(np.array([0,-3.3,0])).scale(0.19)
+ text12 = TextMobject("The point is approaching (0,0) for the values of x which are negative").move_to(np.array([0,-3.3,0])).scale(0.1)
+ text13 = TextMobject("Values of x are tending to 0 from negative side").move_to(np.array([0,-3.3,0])).scale(0.19)
+ text14 = TexMobject(r"\text {Notation for this is }",r"x\rightarrow { 0 }^{ - }").move_to(np.array([0,-3.3,0])).scale(0.25)
+
+
+ self.play(FadeIn(text2), run_time = 1.5)
+ self.wait(2.5)
+ self.setup_axes()
+ graph_1 = self.get_graph(lambda x : x, color = RED, x_min = 0, x_max = 1)
+ graph_2 = self.get_graph(lambda x : -x, color = RED, x_min = 0, x_max = -1)
+ graph_3 = self.get_graph(lambda x : x,color = RED, x_min = 0.005, x_max = 0.03)
+ graph_4 = self.get_graph(lambda x : x,color = GREEN_SCREEN, x_min = 0.03, x_max = 0.005)
+ graph_5 = self.get_graph(lambda x : -x,color = GREEN_SCREEN, x_min = -0.03, x_max = -0.005)
+ grp1 = VGroup(graph_1,graph_2)
+ grp2 = VGroup(brline2, textazero1)
+ grp3 = VGroup(textazero2, textm003, brline3, brline4)
+ self.play(ShowCreation(grp1))
+ self.add(sqr)
+ self.play(ReplacementTransform(text2, text3))
+ self.camera_frame.save_state()
+ self.play(self.camera_frame.set_width,2.25,self.camera_frame.move_to,sqr,run_time = 2)
+ self.wait(2.5)
+ self.play(ReplacementTransform(text3, text4), ShowCreation(dot1))
+ self.wait(2.5)
+ self.play(ReplacementTransform(text4, text5), ShowCreation(brline1), ShowCreation(text003))
+ self.wait(2.5)
+ for i in range(0,3):
+ self.play(MoveAlongPath(dot1,graph_3), run_time = 0.5)
+ self.play(MoveAlongPath(dot1,graph_4), run_time = 0.5)
+ self.play(ReplacementTransform(text5, text6), ShowCreation(grp2))
+ self.wait(2)
+ self.play(FadeOut(dot1))
+ self.add(graph_4)
+ self.play(ReplacementTransform(text6, text7))
+ self.wait(2.5)
+ self.play(ReplacementTransform(text7,text8))
+ for i in range(0,3):
+ self.play(MoveAlongPath(dot1,graph_4), run_time = 0.7)
+ self.play(ReplacementTransform(text8, text9))
+ self.wait(2.5)
+ self.play(ReplacementTransform(text9, text10))
+ self.wait(2.5)
+ self.play(ShowCreation(grp3), ReplacementTransform(text10, text11), FadeOut(dot1))
+ self.add(graph_5)
+ for i in range(0,3):
+ self.play(MoveAlongPath(dot2, graph_5), run_time = 0.7)
+ self.play(ReplacementTransform(text11, text12))
+ self.wait(2.5)
+ self.play(ReplacementTransform(text12, text13))
+ self.wait(2.5)
+ self.play(ReplacementTransform(text13, text14))
+ self.wait(2)
+ self.play(FadeOut(dot2), ReplacementTransform(text14, textdef))
+ self.wait(2)
+ self.play(Restore(self.camera_frame))
+
+ self.wait(2.5)
diff --git a/FSF-2020/calculus/intro-to-calculus/limit/limit3.py b/FSF-2020/calculus/intro-to-calculus/limit/limit3.py
new file mode 100644
index 0000000..a4f07d7
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/limit/limit3.py
@@ -0,0 +1,95 @@
+from manimlib.imports import *
+class limit3(GraphScene, MovingCameraScene):
+ def setup(self):
+ GraphScene.setup(self)
+ MovingCameraScene.setup(self)
+ CONFIG = {
+ "y_max" : 10,
+ "y_min" : 0,
+ "x_max" : 100,
+ "x_min" : 0,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 10,
+ "axes_color" : WHITE,
+ "num_graph_anchor_points": 3000, #this is the number of points that graph manim
+ "graph_origin" : ORIGIN+3*DOWN+4*LEFT,
+ "x_labeled_nums": list(range(0,101))[::10],
+ "y_labeled_nums": list(range(0,11)),
+ "x_axis_label":"$x$",
+ "y_axis_label":"$f(x)$",
+ "x_axis_width": 10,
+ "y_axis_height": 5,
+ }
+ def construct(self):
+ XTD = self.x_axis_width/(self.x_max - self.x_min)
+ YTD = self.y_axis_height/(self.y_max - self.y_min)
+ sqr1 = Square(side_length = 15).move_to(np.array([1,0.5,0]))
+ sqr2 = Square(side_length = 15).move_to(np.array([-4,-3,0]))
+
+ textdef = TextMobject("")
+ text20 = TextMobject("f(x) is not defined at x=50").move_to(np.array([1,0.3,0])).scale(0.2)
+ text21 = TexMobject(r"\text {f(x) is not defined in interval }",r" (-\infty ,\quad 1]").move_to(np.array([-4,-3.2,0])).scale(0.18)
+ text22 = TextMobject("1").move_to(np.array([-3.9,-3.05,0])).scale(0.2)
+ text1 = TexMobject(r"\text {Let }" ,r"f\left( x \right) =\begin{cases} \sqrt { x-1 } ,x\in \quad (1,\infty )-50 \end{cases}")
+ text2 = TextMobject("Graph of f(x) is ")
+ text3 = TextMobject("Right hand neighbour of 50 will approximately be 50.000001").move_to(np.array([1,0.3,0])).scale(0.15)
+ text4 = TextMobject("Left hand neighbour of 50 will approximately be 49.999999").move_to(np.array([1,0.3,0])).scale(0.15)
+ text5 = TexMobject(r"\text {Hence R.H.L }", r"=\lim _{ x\rightarrow { 50 }^{ + } }{ \sqrt { 50.000001 - 1 } } \approx 7.000000071").move_to(np.array([1,0.3,0])).scale(0.13)
+ text6 = TexMobject(r"\text{Hence L.H.L }", r" = \lim _{ x\rightarrow { 50 }^{ - } }{ \sqrt { 49.999999-1 } }\approx 6.999999929").move_to(np.array([1,0.3,0])).scale(0.13)
+ text7 = TextMobject("7.000000071").move_to(np.array([1.9,0.25,0])).scale(0.1)
+ text8 = TextMobject("6.999999929").move_to(np.array([0.1,0.25,0])).scale(0.1)
+ text9 = TexMobject(r"6.999999929\quad \approx \quad 7.000000071 \quad \approx 7").move_to(np.array([1,0.25,0])).scale(0.2)
+ text10 = TexMobject(r"\text{Because LHL }" ,r"\approx" ,r"\text{ RHL, Limit exists at x=50 and equals 7").move_to(np.array([1,0.25,0])).scale(0.13)
+ text11 = TextMobject("There is no Left hand neighbour of x=1").move_to(np.array([-4,-3.2,0])).scale(0.22)
+ text12 = TexMobject(r"\therefore\quad \lim _{ x\rightarrow 0 }{ f(x) } \quad =\quad \lim _{ x\rightarrow { 0 }^{ + } }{ f(x) } ").move_to(np.array([-4,-3.2,0])).scale(0.25)
+ text13 = TexMobject(r"\text {R.H.L =}",r" \lim _{ x\rightarrow { 0 }^{ + } }{ \sqrt { 1.000000000001-1 } } \quad \approx 0").move_to(np.array([-4,-3.2,0])).scale(0.13)
+ text14 = TexMobject(r"\therefore \quad \lim _{ x\rightarrow 0 }{ f(x)\quad =\quad 0 }").move_to(np.array([-4,-3.2,0])).scale(0.13)
+ self.camera_frame.save_state()
+ self.play(ShowCreation(text1))
+ self.wait(3)
+ self.play(ReplacementTransform(text1, text2))
+ self.wait()
+ self.play(ReplacementTransform(text2, textdef))
+ self.setup_axes()
+ self.setup()
+ graph_1 = self.get_graph(lambda x : (x-1)**(1/2),color = PINK, x_min = 1, x_max = 49.9)
+ graph_2 = self.get_graph(lambda x : (x-1)**(1/2),color = PINK, x_min = 50.1, x_max = 100)
+ graph_3 = self.get_graph(lambda x : (x-1)**(1/2),color = PINK, x_min = 1.05, x_max = 1.001)
+ dot1 = SmallDot(color = PURPLE_A)
+ cir = Circle(radius = 0.01, color = GREEN_SCREEN).move_to(np.array([1,0.5,0]))
+ grp1 = VGroup(graph_1, graph_2, cir)
+ grp2 = VGroup(text7, text8)
+ self.play(ShowCreation(grp1))
+ self.wait(2)
+ self.play(self.camera_frame.set_width,2.25,self.camera_frame.move_to,sqr1,run_time = 2)
+ self.wait(1)
+ self.play(ShowCreation(text20))
+ self.wait(2)
+ self.play(ReplacementTransform(text20, text3))
+ self.wait(3)
+ self.play(ReplacementTransform(text3, text5))
+ self.wait(3)
+ self.play(ReplacementTransform(text5, text7), ShowCreation(text4))
+ self.wait(4)
+ self.play(ReplacementTransform(text4, text6))
+ self.wait(3)
+ self.play(ReplacementTransform(text6, text8))
+ self.wait(1.5)
+ self.play(ReplacementTransform(grp2, text9))
+ self.wait(1.5)
+ self.play(ReplacementTransform(text9, text10))
+ self.wait(3)
+ self.play(self.camera_frame.set_width,2.25,self.camera_frame.move_to,sqr2,run_time = 2)
+ self.play(ShowCreation(text21), ShowCreation(text22))
+ self.play(MoveAlongPath(dot1, graph_3), run_time = 3)
+ self.wait(3)
+ self.play(ReplacementTransform(text21, text11))
+ self.wait(3)
+ self.play(ReplacementTransform(text11, text12))
+ self.wait(3)
+ self.play(ReplacementTransform(text12, text13))
+ self.wait(2)
+ self.play(ReplacementTransform(text13, text14))
+ self.wait(3)
+ self.play(ReplacementTransform(text14, textdef))
+ self.wait(2)
diff --git a/FSF-2020/calculus/intro-to-calculus/limit/limitdef.py b/FSF-2020/calculus/intro-to-calculus/limit/limitdef.py
new file mode 100644
index 0000000..15f2845
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/limit/limitdef.py
@@ -0,0 +1,73 @@
+from manimlib.imports import *
+class limitdef(GraphScene, Scene):
+ CONFIG = {
+ "y_max" : 5,
+ "y_min" : 0,
+ "x_max" : 5,
+ "x_min" : -5,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "axes_color" : WHITE,
+ "num_graph_anchor_points": 3000, #this is the number of points that graph manim
+ "graph_origin" : ORIGIN+2*DOWN,
+ "x_labeled_nums": None,#list(range(-1,2)),
+ "y_labeled_nums": None,#list(range(0,2)),
+ "x_axis_label":"$x$",
+ "y_axis_label":"$f(x)$",
+ "x_axis_width": 10,
+ "y_axis_height": 5,
+ }
+ def construct(self):
+ Ldot = MediumDot(self.graph_origin+2.1*UP).set_color(GREEN_SCREEN)
+ adot = MediumDot(self.graph_origin+3*RIGHT).set_color(PINK)
+ epline1 = DashedVMobject(Line(self.graph_origin+1*LEFT+2.5*UP, self.graph_origin+4*RIGHT+2.5*UP))
+ epline2 = DashedVMobject(Line(self.graph_origin+1*LEFT+1.7*UP, self.graph_origin+4*RIGHT+1.7*UP))
+ epline3 = DashedVMobject(Line(self.graph_origin+3.5*RIGHT+0.5*DOWN, self.graph_origin+3.5*RIGHT+2.5*UP))
+ epline4 = DashedVMobject(Line(self.graph_origin+2.5*RIGHT+0.5*DOWN, self.graph_origin+2.5*RIGHT+2.5*UP))
+ Lline = Line(self.graph_origin+2.1*UP, self.graph_origin+3*RIGHT+2.1*UP).set_color(GREEN_SCREEN)
+ aline = Line(self.graph_origin+3*RIGHT, self.graph_origin+3*RIGHT+2.1*UP).set_color(PINK)
+ vertical_rectangle = Rectangle(width = 1, height = 0.8, color = PINK, fill_opacity = 0.5, fill_color = LIGHT_PINK).move_to(self.graph_origin+3*RIGHT+2.1*UP)
+ horizontal_rectangle = Rectangle(width = 1, height = 0.8, color = GREEN_SCREEN, fill_opacity = 0.5, fill_color = GREEN).move_to(self.graph_origin+3*RIGHT+2.1*UP)
+ vec1 = Line(self.graph_origin+2.5*UP, self.graph_origin+2.1*UP)
+ vec2 = Line(self.graph_origin+2.1*UP, self.graph_origin+1.7*UP)
+ vec3 = Line(self.graph_origin+2.5*RIGHT, self.graph_origin+3*RIGHT)
+ vec4 = Line(self.graph_origin+3*RIGHT, self.graph_origin+3.5*RIGHT)
+ brace1 = Brace(vec1, LEFT)
+ brace2 = Brace(vec2, LEFT)
+ brace3 = Brace(vec3, DOWN)
+ brace4 = Brace(vec4, DOWN)
+ br1text = brace1.get_text(r"$\epsilon$").next_to(brace1, LEFT)
+ br2text = brace2.get_text(r"$\epsilon$").next_to(brace2, LEFT)
+ br3text = brace3.get_text(r"$\delta$").next_to(brace3, DOWN)
+ br4text = brace4.get_text(r"$\delta$").next_to(brace4, DOWN)
+ epgrp = VGroup(epline1, epline2, Ldot, adot, Lline, aline, epline4, epline3)
+ recgrp = VGroup(vertical_rectangle, horizontal_rectangle)
+ epbrgrp = VGroup(brace1, brace2, br1text, br2text)
+ delbrgrp = VGroup(brace3, brace4, br3text, br4text)
+ self.setup_axes()
+ graph_1 = self.get_graph(lambda x :0.1*(x+1)**2 +0.5, x_min = -5, x_max = 5)
+ graph_2 = self.get_graph(lambda x : 0.1*(x+1)**2 +0.5, x_min = 2.5, x_max = 3.5, color = YELLOW_A)
+ graph_2.shift(2.5*LEFT)
+ self.play(ShowCreation(graph_1))
+ self.wait(2)
+ self.play(ShowCreation(epgrp), ShowCreation(horizontal_rectangle), ShowCreation(vertical_rectangle))
+ self.wait(2)
+ self.play(ShowCreation(epbrgrp))
+ self.play(ShowCreation(delbrgrp))
+ self.wait(2)
+ self.play(FadeOut(recgrp))
+ self.wait(2)
+ for i in range(0,1):
+ self.play(ApplyMethod(graph_2.shift, 2.5*RIGHT))
+ self.wait(1)
+ self.play(ApplyMethod(graph_2.shift, 1.7*DOWN))
+ self.play(ApplyMethod(graph_2.shift, 1.7*UP))
+ self.wait(1)
+ self.play(ApplyMethod(graph_2.shift, 2.5*LEFT))
+ self.play(ApplyMethod(graph_2.shift, 2.5*RIGHT))
+ self.wait(1)
+ self.play(ApplyMethod(graph_2.shift, 1.7*DOWN))
+ self.play(ApplyMethod(graph_2.shift, 1.7*UP))
+ self.wait(1)
+ self.play(ApplyMethod(graph_2.shift, 2.5*LEFT))
+ self.wait()
generated by cgit (git 2.34.1) at 2025-02-19 08:22:55 +0000