Adjusted limits animation and cleaned up the folders

calc-backend/animation-gen/derivativeAnimation.py

@@ -67,4 +67,6 @@ def construct(self):
         self.play(x.animate(rate_func=linear).set_value(3), run_time = 1.5)
         self.play(x.animate(rate_func=rush_from).set_value(1), run_time = 2)
         self.play(x.animate(rate_func=rush_into).set_value(3), run_time = 2)
-        self.play(x.animate(rate_func=linear).set_value(5.5), run_time = 1.5)
+        self.play(x.animate(rate_func=linear).set_value(5.5), run_time = 1.5)
+
+        self.wait(3)

calc-backend/animation-gen/integralAnimation.py

@@ -20,18 +20,15 @@ def construct(self):
 
         self.add(axes, x_label, y_label)
 
-        # Plot y = 0.6 * x^2 from 0 to 2.6
         graph = axes.plot(lambda x: 0.6 * x**2, x_range=[0, 2.3], color=WHITE)
         self.play(Create(graph), run_time=1)
 
-        # Riemann sum parameters
         a, b = 0, 2
         n = 10
         dx = (b - a) / n
         rectangles = VGroup()
         area_sum = 0
 
-        # Create rectangles using f(x) = 0.6 * x^2
         for i in range(1, n + 1):
             x_right = a + i * dx
             height = 0.6 * x_right**2
@@ -55,17 +52,17 @@ def construct(self):
         for rect in rectangles:
             self.play(FadeIn(rect, run_time=0.15))
 
-        # Show area label in top-right corner
         area_text = Text(f"Area ≈ {area_sum:.2f}", font_size=36)
         area_text.to_edge(UP).shift(DOWN*2.4 + LEFT * 3.5)
         self.play(Write(area_text))
 
         self.wait(1.5)
-
-        # Fade everything out
+
         self.play(
             FadeOut(rectangles),
             FadeOut(area_text),
             FadeOut(graph),
             run_time=1
         )
+
+        self.wait(3)

calc-backend/animation-gen/limitsAnimation.py

@@ -0,0 +1,81 @@
+import numpy as np   
+from manim import *
+
+class Limit(Scene):
+    def construct(self):
+
+        axes = Axes(
+            x_range=[0.1, 4, 1],
+            y_range=[0, 10, 2],
+            axis_config={"include_numbers": True},
+            x_length=8,
+            y_length=5
+        )
+        labels = axes.get_axis_labels(x_label="x", y_label="y")
+        self.play(Create(axes), Write(labels))
+
+        def func(x):
+            if x == 2:
+                return np.nan  # removable discontinuity
+            return (x**2 + 4*x - 12)/(x**2 - 2*x)
+
+        graph = axes.plot(
+            func, 
+            color=WHITE, 
+            discontinuities=[2], 
+            dt=0.01,
+            x_range=[.7, 3.9]
+        )
+
+        hole_point = Circle(
+            radius=0.04,
+            color=WHITE,
+            fill_opacity=0,
+            stroke_width=4
+        ).move_to(axes.c2p(2, func(2.01)))
+
+        self.play(Create(graph), FadeIn(hole_point), run_time=2)
+
+        # ValueTrackers for dynamic movement
+        t_left = ValueTracker(0.7)
+        t_right = ValueTracker(3.5)
+
+        # Initial dummy arrows
+        left_arrow = always_redraw(lambda: Arrow(
+            start=axes.c2p(0.7, func(0.7) + 0.3),
+            end=axes.c2p(t_left.get_value(), func(t_left.get_value())),
+            color=BLUE,
+            stroke_width=6,
+            buff=0
+        ))
+
+        right_arrow = always_redraw(lambda: Arrow(
+            start=axes.c2p(3.5, func(3.5) + 0.3),
+            end=axes.c2p(t_right.get_value(), func(t_right.get_value())),
+            color=YELLOW,
+            stroke_width=6,
+            buff=0
+        ))
+
+        self.add(left_arrow, right_arrow)
+
+        # Animate trackers to move arrows toward x = 2
+        self.play(
+            t_left.animate.set_value(1.99),
+            t_right.animate.set_value(2.01),
+            run_time=2,
+            rate_func=linear
+        )
+
+        self.wait(0.5)
+
+        self.play(
+            FadeOut(axes),
+            FadeOut(labels),
+            FadeOut(graph),
+            FadeOut(hole_point),
+            FadeOut(left_arrow),
+            FadeOut(right_arrow)
+        )
+
+        self.wait(3)

calc-frontend/package.json

@@ -17,7 +17,7 @@
     "@radix-ui/react-tooltip": "^1.2.0",
     "@tailwindcss/vite": "^4.0.4",
     "axios": "^1.8.1",
-    "better-auth": "^1.2.4",
+    "better-auth": "^1.2.7",
     "class-variance-authority": "^0.7.1",
     "clsx": "^2.1.1",
     "jsdom": "^26.0.0",

calc-frontend/src/animations/animations_etc/media/Tex/66e1bc57a83e0f07.tex

@@ -0,0 +1,9 @@
+\documentclass[preview]{standalone}
+\usepackage[english]{babel}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\begin{document}
+\begin{align*}
+0
+\end{align*}
+\end{document}

calc-frontend/src/animations/animations_etc/media/Tex/70b3a8630e8c4922.tex

@@ -0,0 +1,9 @@
+\documentclass[preview]{standalone}
+\usepackage[english]{babel}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\begin{document}
+\begin{align*}
+f(x)
+\end{align*}
+\end{document}

calc-frontend/src/animations/animations_etc/media/Tex/b330e3953bf029d7.tex

@@ -0,0 +1,9 @@
+\documentclass[preview]{standalone}
+\usepackage[english]{babel}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\begin{document}
+\begin{align*}
+6
+\end{align*}
+\end{document}

calc-frontend/src/animations/animations_etc/media/Tex/b47c9feb1c667bc8.tex

@@ -0,0 +1,9 @@
+\documentclass[preview]{standalone}
+\usepackage[english]{babel}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\begin{document}
+\begin{align*}
+8
+\end{align*}
+\end{document}

calc-frontend/src/animations/manim-videos/limitsAnimation/1080p60/partial_movie_files/Limit/partial_movie_file_list.txt

@@ -0,0 +1,7 @@
+# This file is used internally by FFMPEG.
+file 'file:/home/drake/CalculusVisualizerProject/calc-visualizer/calc-backend/animation-gen/media/videos/limitsAnimation/1080p60/partial_movie_files/Limit/3529212410_1240247844_223132457.mp4'
+file 'file:/home/drake/CalculusVisualizerProject/calc-visualizer/calc-backend/animation-gen/media/videos/limitsAnimation/1080p60/partial_movie_files/Limit/3040924799_1376512726_2967433267.mp4'
+file 'file:/home/drake/CalculusVisualizerProject/calc-visualizer/calc-backend/animation-gen/media/videos/limitsAnimation/1080p60/partial_movie_files/Limit/3040924799_2510802644_669525166.mp4'
+file 'file:/home/drake/CalculusVisualizerProject/calc-visualizer/calc-backend/animation-gen/media/videos/limitsAnimation/1080p60/partial_movie_files/Limit/3040924799_2341082278_949554925.mp4'
+file 'file:/home/drake/CalculusVisualizerProject/calc-visualizer/calc-backend/animation-gen/media/videos/limitsAnimation/1080p60/partial_movie_files/Limit/3040924799_1333778094_730062091.mp4'
+file 'file:/home/drake/CalculusVisualizerProject/calc-visualizer/calc-backend/animation-gen/media/videos/limitsAnimation/1080p60/partial_movie_files/Limit/3040924799_4166842112_3149261676.mp4'

calc-frontend/src/animations/manim-videos/limitsAnimation/480p15/partial_movie_files/Limit/partial_movie_file_list.txt

@@ -0,0 +1,7 @@
+# This file is used internally by FFMPEG.
+file 'file:/home/drake/CalculusVisualizerProject/calc-visualizer/calc-backend/animation-gen/media/videos/limitsAnimation/480p15/partial_movie_files/Limit/1185818338_1240247844_223132457.mp4'
+file 'file:/home/drake/CalculusVisualizerProject/calc-visualizer/calc-backend/animation-gen/media/videos/limitsAnimation/480p15/partial_movie_files/Limit/624642324_1376512726_2967433267.mp4'
+file 'file:/home/drake/CalculusVisualizerProject/calc-visualizer/calc-backend/animation-gen/media/videos/limitsAnimation/480p15/partial_movie_files/Limit/624642324_2510802644_4234489363.mp4'
+file 'file:/home/drake/CalculusVisualizerProject/calc-visualizer/calc-backend/animation-gen/media/videos/limitsAnimation/480p15/partial_movie_files/Limit/624642324_2341082278_384939764.mp4'
+file 'file:/home/drake/CalculusVisualizerProject/calc-visualizer/calc-backend/animation-gen/media/videos/limitsAnimation/480p15/partial_movie_files/Limit/624642324_960113373_1562076290.mp4'
+file 'file:/home/drake/CalculusVisualizerProject/calc-visualizer/calc-backend/animation-gen/media/videos/limitsAnimation/480p15/partial_movie_files/Limit/624642324_4166842112_3149261676.mp4'

calc-frontend/src/pages/Home.tsx

@@ -5,6 +5,7 @@ import SignInButton from "../components/ui/SignInButton";
 import SignOutButton from "../components/ui/SignOutButton";
 import derivativeVideo from '../animations/manim-videos/derivativeAnimation/1080p60/DerivativeAnimation.mp4';
 import integralVideo from '../animations/manim-videos/integralAnimation/1080p60/RightRiemannSum.mp4';
+import limitVideo from '../animations/manim-videos/limitsAnimation/1080p60/Limit.mp4';
 
 function Home() {
   const { session, isPending } = useAuth();
@@ -91,7 +92,7 @@ function Home() {
 
       <video
         className="w-full object-cover rounded-t-md"
-        src={derivativeVideo}
+        src={limitVideo}
         autoPlay
         loop
         muted