pull request

14 files changed, 146 insertions, 73 deletions

diff --git a/FSF-2020/calculus/intro-to-calculus/gabrielshorn/gabriel1.py b/FSF-2020/calculus/intro-to-calculus/gabriels-horn/gabriel1.py
index 3596c88..3596c88 100644
--- a/FSF-2020/calculus/intro-to-calculus/gabrielshorn/gabriel1.py
+++ b/FSF-2020/calculus/intro-to-calculus/gabriels-horn/gabriel1.py
diff --git a/FSF-2020/calculus/intro-to-calculus/gabrielshorn/gabriel2.py b/FSF-2020/calculus/intro-to-calculus/gabriels-horn/gabriel2.py
index 1e2a820..1e2a820 100644
--- a/FSF-2020/calculus/intro-to-calculus/gabrielshorn/gabriel2.py
+++ b/FSF-2020/calculus/intro-to-calculus/gabriels-horn/gabriel2.py
diff --git a/FSF-2020/calculus/intro-to-calculus/introderivative/derivative1.py b/FSF-2020/calculus/intro-to-calculus/intro-to-derivative/derivative1.py
index 79a6fc6..79a6fc6 100644
--- a/FSF-2020/calculus/intro-to-calculus/introderivative/derivative1.py
+++ b/FSF-2020/calculus/intro-to-calculus/intro-to-derivative/derivative1.py
diff --git a/FSF-2020/calculus/intro-to-calculus/introderivative/derivative2.py b/FSF-2020/calculus/intro-to-calculus/intro-to-derivative/derivative2.py
index d6aab15..d6aab15 100644
--- a/FSF-2020/calculus/intro-to-calculus/introderivative/derivative2.py
+++ b/FSF-2020/calculus/intro-to-calculus/intro-to-derivative/derivative2.py
diff --git a/FSF-2020/calculus/intro-to-calculus/introderivative/derivative3.py b/FSF-2020/calculus/intro-to-calculus/intro-to-derivative/derivative3.py
index ebbacb1..ebbacb1 100644
--- a/FSF-2020/calculus/intro-to-calculus/introderivative/derivative3.py
+++ b/FSF-2020/calculus/intro-to-calculus/intro-to-derivative/derivative3.py
diff --git a/FSF-2020/calculus/intro-to-calculus/limit/limitdef.py b/FSF-2020/calculus/intro-to-calculus/limit/limitdef.py
deleted file mode 100644
index 15f2845..0000000
--- a/FSF-2020/calculus/intro-to-calculus/limit/limitdef.py
+++ /dev/null
@@ -1,73 +0,0 @@
-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()
diff --git a/FSF-2020/calculus/intro-to-calculus/limit/limitfin1.py b/FSF-2020/calculus/intro-to-calculus/limit/limitfin1.py
new file mode 100644
index 0000000..ba57a15
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/limit/limitfin1.py
@@ -0,0 +1,76 @@
+from manimlib.imports import *
+class limitfin1(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,
+        "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: x**3 +1.5, x_min = self.x_min, x_max = -0.1)
+        graph2 = self.get_graph(lambda x: x**3 +1.5, x_min = 0.1, x_max = self.x_max, color = self.graph_color)
+        dot2 = Circle(radius = 0.1).move_to(self.graph_origin+1.5*UP*YTD)
+        text0 = TextMobject("Let L be the value of f(x) at point denoted by circle").move_to(self.graph_origin+2*DOWN)
+        text1 = TexMobject(r"\text{As }", r"\delta",r"\text{ tends to zero }" ,r"\epsilon" r"\text{ tends to zero}").move_to(self.graph_origin+2*DOWN)
+        text2 = TexMobject(r"\text{For all values in }", r"(-\delta, +\delta)",r"\text{ you will always find a real and finite value of f(x) in }",r"(L-\epsilon, L+\epsilon)").move_to(self.graph_origin+2*DOWN).scale(0.6)
+        self.play(ShowCreation(graph1), ShowCreation(graph2), ShowCreation(text0), 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(ReplacementTransform(text0, text1))
+        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+1.6*UP*YTD+4*RIGHT*XTD, self.graph_origin+1.5*UP*YTD+4*RIGHT*XTD)
+        vec8 = Line(self.graph_origin+1.4*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, 1.8*UP*XTD), 
+            ApplyMethod(line5.shift, 1.8*DOWN*XTD))
+        self.wait(3)
+        self.play(ReplacementTransform(text1, text2))
+        self.play(FadeOut(brace5), FadeOut(brace6), 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),
+            ApplyMethod(line5.shift, 1.8*UP*XTD), ApplyMethod(line4.shift, 1.8*DOWN*XTD))
+        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),
+            ApplyMethod(line5.shift, 1.8*DOWN*XTD), ApplyMethod(line4.shift, 1.8*UP*XTD), ApplyMethod(br5text.scale, 0.3), ApplyMethod(br6text.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),
+            ApplyMethod(line5.shift, 1.8*UP*XTD), ApplyMethod(line4.shift, 1.8*DOWN*XTD), ApplyMethod(br5text.scale, 10/3), ApplyMethod(br6text.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),
+            ApplyMethod(line5.shift, 1.8*DOWN*XTD), ApplyMethod(line4.shift, 1.8*UP*XTD),ApplyMethod(br5text.scale, 0.3), ApplyMethod(br6text.scale, 0.3), run_time = 0.5)
+
+        self.wait(5)
\ No newline at end of file
diff --git a/FSF-2020/calculus/intro-to-calculus/limit/limitfin2.py b/FSF-2020/calculus/intro-to-calculus/limit/limitfin2.py
new file mode 100644
index 0000000..36ca388
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/limit/limitfin2.py
@@ -0,0 +1,70 @@
+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)
\ No newline at end of file
diff --git a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/README.md b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/README.md
index a9ad0bb..a9ad0bb 100644
--- a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/README.md
+++ b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/README.md
diff --git a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/RiemannRectanglesAnimation.py b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/RiemannRectanglesAnimation.py
index 1757231..1757231 100644
--- a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/RiemannRectanglesAnimation.py
+++ b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/RiemannRectanglesAnimation.py
diff --git a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/mimi.py b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/mimi.py
index 2471c87..2471c87 100644
--- a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/mimi.py
+++ b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/mimi.py
diff --git a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect1.py b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/rierect1.py
index 748d766..748d766 100644
--- a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect1.py
+++ b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/rierect1.py
diff --git a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect2.py b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/rierect2.py
index e300250..e300250 100644
--- a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect2.py
+++ b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/rierect2.py
diff --git a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect3.py b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/rierect3.py
index 3542358..3542358 100644
--- a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/rierect3.py
+++ b/FSF-2020/calculus/intro-to-calculus/riemann-integrals/rierect3.py