diff --git a/calc-frontend/package-lock.json b/calc-frontend/package-lock.json
index 7c5a677..6bf894f 100644
--- a/calc-frontend/package-lock.json
+++ b/calc-frontend/package-lock.json
@@ -14,7 +14,7 @@
"@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",
@@ -3245,29 +3245,28 @@
"license": "MIT"
},
"node_modules/better-auth": {
- "version": "1.2.5",
- "resolved": "https://registry.npmjs.org/better-auth/-/better-auth-1.2.5.tgz",
- "integrity": "sha512-Tz2aKImkvaT7P9qHQ67Vhw/Slo6zpvE0jG7GoDQM+dd5tWuC3lP0OGjjWkNCZdToVlWB193i5nSHeZT90sFqEw==",
+ "version": "1.2.7",
+ "resolved": "https://registry.npmjs.org/better-auth/-/better-auth-1.2.7.tgz",
+ "integrity": "sha512-2hCB263GSrgetsMUZw8vv9O1e4S4AlYJW3P4e8bX9u3Q3idv4u9BzDFCblpTLuL4YjYovghMCN0vurAsctXOAQ==",
"dependencies": {
"@better-auth/utils": "0.2.4",
- "@better-fetch/fetch": "^1.1.17",
+ "@better-fetch/fetch": "^1.1.18",
"@noble/ciphers": "^0.6.0",
"@noble/hashes": "^1.6.1",
"@simplewebauthn/browser": "^13.0.0",
"@simplewebauthn/server": "^13.0.0",
- "better-call": "^1.0.5",
+ "better-call": "^1.0.8",
"defu": "^6.1.4",
"jose": "^5.9.6",
"kysely": "^0.27.6",
"nanostores": "^0.11.3",
- "valibot": "1.0.0-beta.15",
"zod": "^3.24.1"
}
},
"node_modules/better-call": {
- "version": "1.0.7",
- "resolved": "https://registry.npmjs.org/better-call/-/better-call-1.0.7.tgz",
- "integrity": "sha512-p5kEthErx3HsW9dCCvvEx+uuEdncn0ZrlqrOG3TkR1aVYgynpwYbTVU90nY8/UwfMhROzqZWs8vryainSQxrNg==",
+ "version": "1.0.8",
+ "resolved": "https://registry.npmjs.org/better-call/-/better-call-1.0.8.tgz",
+ "integrity": "sha512-/PV8JLqDRUN7JyBPbklVsS/8E4SO3pnf8hbpa8B7xrBrr+BBYpeOAxoqtnsyk/pRs35vNB4MZx8cn9dBuNlLDA==",
"dependencies": {
"@better-fetch/fetch": "^1.1.4",
"rou3": "^0.5.1",
@@ -10190,7 +10189,7 @@
"version": "5.6.3",
"resolved": "https://registry.npmjs.org/typescript/-/typescript-5.6.3.tgz",
"integrity": "sha512-hjcS1mhfuyi4WW8IWtjP7brDrG2cuDZukyrYrSauoXGNgx0S7zceP07adYkJycEr56BOUTNPzbInooiN3fn1qw==",
- "devOptional": true,
+ "dev": true,
"license": "Apache-2.0",
"bin": {
"tsc": "bin/tsc",
@@ -10395,20 +10394,6 @@
}
}
},
- "node_modules/valibot": {
- "version": "1.0.0-beta.15",
- "resolved": "https://registry.npmjs.org/valibot/-/valibot-1.0.0-beta.15.tgz",
- "integrity": "sha512-BKy8XosZkDHWmYC+cJG74LBzP++Gfntwi33pP3D3RKztz2XV9jmFWnkOi21GoqARP8wAWARwhV6eTr1JcWzjGw==",
- "license": "MIT",
- "peerDependencies": {
- "typescript": ">=5"
- },
- "peerDependenciesMeta": {
- "typescript": {
- "optional": true
- }
- }
- },
"node_modules/vfile": {
"version": "6.0.3",
"resolved": "https://registry.npmjs.org/vfile/-/vfile-6.0.3.tgz",
diff --git a/calc-frontend/package.json b/calc-frontend/package.json
index b45c9be..2c5bfde 100644
--- a/calc-frontend/package.json
+++ b/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",
diff --git a/calc-frontend/src/Animations/__pycache__/derivativeAnimation.cpython-310.pyc b/calc-frontend/src/Animations/__pycache__/derivativeAnimation.cpython-310.pyc
index edb8108..6120aea 100644
Binary files a/calc-frontend/src/Animations/__pycache__/derivativeAnimation.cpython-310.pyc and b/calc-frontend/src/Animations/__pycache__/derivativeAnimation.cpython-310.pyc differ
diff --git a/calc-frontend/src/Animations/__pycache__/integralAnimations.cpython-310.pyc b/calc-frontend/src/Animations/__pycache__/integralAnimations.cpython-310.pyc
new file mode 100644
index 0000000..0561990
Binary files /dev/null and b/calc-frontend/src/Animations/__pycache__/integralAnimations.cpython-310.pyc differ
diff --git a/calc-frontend/src/Animations/__pycache__/limitsAnimation.cpython-310.pyc b/calc-frontend/src/Animations/__pycache__/limitsAnimation.cpython-310.pyc
new file mode 100644
index 0000000..51b2091
Binary files /dev/null and b/calc-frontend/src/Animations/__pycache__/limitsAnimation.cpython-310.pyc differ
diff --git a/calc-frontend/src/Animations/derivativeAnimation.py b/calc-frontend/src/Animations/derivativeAnimation.py
index d84d957..aafc4b6 100644
--- a/calc-frontend/src/Animations/derivativeAnimation.py
+++ b/calc-frontend/src/Animations/derivativeAnimation.py
@@ -18,7 +18,7 @@ def construct(self):
func = axes.plot(
lambda x: .5 * x * (x-3) * (x-4) + .6,
- x_range = (0,10)
+ x_range = (0,5)
)
x = ValueTracker(7)
@@ -38,7 +38,7 @@ def construct(self):
)
)
- dot1 =always_redraw(
+ dot1 = always_redraw(
lambda: Dot()
.scale(0.7)
.move_to(axes.c2p(x.get_value(), func.underlying_function(x.get_value())))
@@ -55,12 +55,18 @@ def construct(self):
)
)
+ tangent_label = always_redraw(
+ lambda: MathTex("y = f'(x)")
+ .scale(0.6)
+ .next_to(secant, UP, buff=0.1)
+ .set_color(GREEN)
+ )
+
self.add(axes, axes_labels,func)
- self.play(Create(VGroup(dot1,dot2,secant)))
+ self.add(dot1,dot2,secant,tangent_label)
self.play(dx.animate.set_value(.001), run_time=1)
- self.wait(2)
self.play(x.animate.set_value(1), run_time = 4)
self.play(x.animate.set_value(7), run_time = 4)
- self.wait()
- self.play(dx.animate.set_value(2), run_time = 4)
- self.wait()
+ self.play(dx.animate.set_value(2), run_time = 1)
+
+ self.wait(3)
\ No newline at end of file
diff --git a/calc-frontend/src/Animations/integralAnimations.py b/calc-frontend/src/Animations/integralAnimations.py
new file mode 100644
index 0000000..08ca1a1
--- /dev/null
+++ b/calc-frontend/src/Animations/integralAnimations.py
@@ -0,0 +1,65 @@
+from manim import *
+
+class RightRiemannSum(Scene):
+ def construct(self):
+ axes = Axes(
+ x_range=[0, 2.5, 1],
+ y_range=[0, 5, 1],
+ x_length=10,
+ y_length=5,
+ axis_config={"include_numbers": True}
+ ).to_edge(LEFT)
+
+ x_label = axes.get_x_axis_label("x")
+ y_label = axes.get_y_axis_label("y")
+
+ self.play(Create(axes), Write(x_label), Write(y_label))
+
+ graph = axes.plot(lambda x: 0.6 * x**2, x_range=[0, 2.3], color=WHITE)
+ self.play(Create(graph), run_time=2)
+
+ a, b = 0, 2
+ n = 10
+ dx = (b - a) / n
+ rectangles = VGroup()
+ area_sum = 0
+
+ for i in range(1, n + 1):
+ x_right = a + i * dx
+ height = 0.6 * x_right**2
+ area_sum += height * dx
+
+ rect_corner = axes.c2p(x_right - dx, 0)
+ rect_width = axes.c2p(dx, 0)[0] - axes.c2p(0, 0)[0]
+ rect_height = axes.c2p(0, height)[1] - axes.c2p(0, 0)[1]
+
+ rect = Rectangle(
+ width=rect_width,
+ height=rect_height,
+ fill_color=YELLOW,
+ fill_opacity=0.8,
+ stroke_width=0.5
+ )
+ rect.align_to(rect_corner, DOWN + LEFT)
+ rectangles.add(rect)
+
+ for rect in rectangles:
+ self.play(FadeIn(rect, run_time=0.2))
+
+ 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)
+
+ self.play(
+ FadeOut(rectangles),
+ FadeOut(area_text),
+ FadeOut(graph),
+ FadeOut(axes),
+ FadeOut(x_label),
+ FadeOut(y_label),
+ run_time=1
+ )
+
+ self.wait(3)
\ No newline at end of file
diff --git a/calc-frontend/src/Animations/limitsAnimation.py b/calc-frontend/src/Animations/limitsAnimation.py
new file mode 100644
index 0000000..9132dd7
--- /dev/null
+++ b/calc-frontend/src/Animations/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)
+
+ def get_tangent_angle(x):
+ dx = 0.001
+ dy = func(x + dx) - func(x)
+ return np.arctan2(dy, dx)
+
+ t_left = ValueTracker(0.7)
+ t_right = ValueTracker(3.5)
+
+ left_arrow = Triangle(color=GREEN, fill_opacity=1).scale(0.2)
+ left_arrow.rotate(PI/2)
+ left_updater = always_redraw(
+ lambda: left_arrow.move_to(axes.c2p(t_left.get_value(), func(t_left.get_value())))
+ .set_angle(get_tangent_angle(t_left.get_value()))
+ )
+
+ right_arrow = Triangle(color=YELLOW, fill_opacity=1).scale(0.2)
+ right_arrow.rotate(PI/2)
+ right_updater = always_redraw(
+ lambda: right_arrow.move_to(axes.c2p(t_right.get_value(), func(t_right.get_value())))
+ .set_angle(get_tangent_angle(t_right.get_value()))
+ )
+
+ self.add(left_updater, right_updater)
+
+ self.play(
+ t_left.animate.set_value(1.99),
+ t_right.animate.set_value(2.01),
+ run_time=2,
+ rate_func=linear
+ )
+
+ self.wait(.5)
+
+ self.play(
+ FadeOut(axes),
+ FadeOut(labels),
+ FadeOut(graph),
+ FadeOut(hole_point),
+ FadeOut(left_arrow),
+ FadeOut(right_arrow)
+ )
+
+ self.wait(3)
diff --git a/calc-frontend/src/Animations/media/Tex/66e1bc57a83e0f07.svg b/calc-frontend/src/Animations/media/Tex/66e1bc57a83e0f07.svg
new file mode 100644
index 0000000..56f9bee
--- /dev/null
+++ b/calc-frontend/src/Animations/media/Tex/66e1bc57a83e0f07.svg
@@ -0,0 +1,10 @@
+
+
+
\ No newline at end of file
diff --git a/calc-frontend/src/Animations/media/Tex/66e1bc57a83e0f07.tex b/calc-frontend/src/Animations/media/Tex/66e1bc57a83e0f07.tex
new file mode 100644
index 0000000..7f5e239
--- /dev/null
+++ b/calc-frontend/src/Animations/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}
\ No newline at end of file
diff --git a/calc-frontend/src/Animations/media/Tex/70b3a8630e8c4922.svg b/calc-frontend/src/Animations/media/Tex/70b3a8630e8c4922.svg
new file mode 100644
index 0000000..c446861
--- /dev/null
+++ b/calc-frontend/src/Animations/media/Tex/70b3a8630e8c4922.svg
@@ -0,0 +1,16 @@
+
+
+
\ No newline at end of file
diff --git a/calc-frontend/src/Animations/media/Tex/70b3a8630e8c4922.tex b/calc-frontend/src/Animations/media/Tex/70b3a8630e8c4922.tex
new file mode 100644
index 0000000..79bedbc
--- /dev/null
+++ b/calc-frontend/src/Animations/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}
\ No newline at end of file
diff --git a/calc-frontend/src/Animations/media/Tex/b330e3953bf029d7.svg b/calc-frontend/src/Animations/media/Tex/b330e3953bf029d7.svg
new file mode 100644
index 0000000..a4e8630
--- /dev/null
+++ b/calc-frontend/src/Animations/media/Tex/b330e3953bf029d7.svg
@@ -0,0 +1,10 @@
+
+
+
\ No newline at end of file
diff --git a/calc-frontend/src/Animations/media/Tex/b330e3953bf029d7.tex b/calc-frontend/src/Animations/media/Tex/b330e3953bf029d7.tex
new file mode 100644
index 0000000..7675c00
--- /dev/null
+++ b/calc-frontend/src/Animations/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}
\ No newline at end of file
diff --git a/calc-frontend/src/Animations/media/Tex/b47c9feb1c667bc8.svg b/calc-frontend/src/Animations/media/Tex/b47c9feb1c667bc8.svg
new file mode 100644
index 0000000..b587f57
--- /dev/null
+++ b/calc-frontend/src/Animations/media/Tex/b47c9feb1c667bc8.svg
@@ -0,0 +1,10 @@
+
+
+
\ No newline at end of file
diff --git a/calc-frontend/src/Animations/media/Tex/b47c9feb1c667bc8.tex b/calc-frontend/src/Animations/media/Tex/b47c9feb1c667bc8.tex
new file mode 100644
index 0000000..b628b4c
--- /dev/null
+++ b/calc-frontend/src/Animations/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}
\ No newline at end of file
diff --git a/calc-frontend/src/Animations/media/Tex/d478985f814b9623.svg b/calc-frontend/src/Animations/media/Tex/d478985f814b9623.svg
new file mode 100644
index 0000000..a73597f
--- /dev/null
+++ b/calc-frontend/src/Animations/media/Tex/d478985f814b9623.svg
@@ -0,0 +1,22 @@
+
+
+
\ No newline at end of file
diff --git a/calc-frontend/src/Animations/media/Tex/d478985f814b9623.tex b/calc-frontend/src/Animations/media/Tex/d478985f814b9623.tex
new file mode 100644
index 0000000..9167c45
--- /dev/null
+++ b/calc-frontend/src/Animations/media/Tex/d478985f814b9623.tex
@@ -0,0 +1,9 @@
+\documentclass[preview]{standalone}
+\usepackage[english]{babel}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\begin{document}
+\begin{align*}
+y = f'(x)
+\end{align*}
+\end{document}
\ No newline at end of file
diff --git a/calc-frontend/src/Animations/media/texts/d6c906d16ecee941.svg b/calc-frontend/src/Animations/media/texts/d6c906d16ecee941.svg
new file mode 100644
index 0000000..dff0242
--- /dev/null
+++ b/calc-frontend/src/Animations/media/texts/d6c906d16ecee941.svg
@@ -0,0 +1,55 @@
+
+
diff --git a/calc-frontend/src/Animations/media/texts/db36c31801db18f7.svg b/calc-frontend/src/Animations/media/texts/db36c31801db18f7.svg
new file mode 100644
index 0000000..d5ae4af
--- /dev/null
+++ b/calc-frontend/src/Animations/media/texts/db36c31801db18f7.svg
@@ -0,0 +1,55 @@
+
+
diff --git a/calc-frontend/src/Animations/media/videos/derivativeAnimation/1080p60/DerivativeAnimation.mp4 b/calc-frontend/src/Animations/media/videos/derivativeAnimation/1080p60/DerivativeAnimation.mp4
index 8f4490f..9bc5ed0 100644
Binary files a/calc-frontend/src/Animations/media/videos/derivativeAnimation/1080p60/DerivativeAnimation.mp4 and b/calc-frontend/src/Animations/media/videos/derivativeAnimation/1080p60/DerivativeAnimation.mp4 differ
diff --git a/calc-frontend/src/Animations/media/videos/derivativeAnimation/1080p60/partial_movie_files/DerivativeAnimation/3040924799_1428517652_1613872388.mp4 b/calc-frontend/src/Animations/media/videos/derivativeAnimation/1080p60/partial_movie_files/DerivativeAnimation/3040924799_1428517652_1613872388.mp4
new file mode 100644
index 0000000..f0139d7
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new file mode 100644
index 0000000..9abf5e0
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diff --git a/calc-frontend/src/Animations/media/videos/derivativeAnimation/1080p60/partial_movie_files/DerivativeAnimation/partial_movie_file_list.txt b/calc-frontend/src/Animations/media/videos/derivativeAnimation/1080p60/partial_movie_files/DerivativeAnimation/partial_movie_file_list.txt
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--- a/calc-frontend/src/Animations/media/videos/derivativeAnimation/1080p60/partial_movie_files/DerivativeAnimation/partial_movie_file_list.txt
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diff --git a/calc-frontend/src/Animations/media/videos/derivativeAnimation/480p15/partial_movie_files/DerivativeAnimation/partial_movie_file_list.txt b/calc-frontend/src/Animations/media/videos/derivativeAnimation/480p15/partial_movie_files/DerivativeAnimation/partial_movie_file_list.txt
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--- /dev/null
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+# This file is used internally by FFMPEG.
+file 'file:/home/drake/CalculusVisualizerProject/calc-visualizer/calc-frontend/src/Animations/media/videos/limitsAnimation/1080p60/partial_movie_files/Limit/3529212410_1240247844_223132457.mp4'
+file 'file:/home/drake/CalculusVisualizerProject/calc-visualizer/calc-frontend/src/Animations/media/videos/limitsAnimation/1080p60/partial_movie_files/Limit/3040924799_1376512726_2967433267.mp4'
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+file 'file:/home/drake/CalculusVisualizerProject/calc-visualizer/calc-frontend/src/Animations/media/videos/limitsAnimation/1080p60/partial_movie_files/Limit/3040924799_960113373_1562076290.mp4'
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diff --git a/calc-frontend/src/Animations/media/videos/limitsAnimation/480p15/partial_movie_files/Limit/624642324_667144672_4176259698.mp4 b/calc-frontend/src/Animations/media/videos/limitsAnimation/480p15/partial_movie_files/Limit/624642324_667144672_4176259698.mp4
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diff --git a/calc-frontend/src/Animations/media/videos/limitsAnimation/480p15/partial_movie_files/Limit/624642324_858855158_1247583088.mp4 b/calc-frontend/src/Animations/media/videos/limitsAnimation/480p15/partial_movie_files/Limit/624642324_858855158_1247583088.mp4
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diff --git a/calc-frontend/src/Animations/media/videos/limitsAnimation/480p15/partial_movie_files/Limit/624642324_960113373_270917492.mp4 b/calc-frontend/src/Animations/media/videos/limitsAnimation/480p15/partial_movie_files/Limit/624642324_960113373_270917492.mp4
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index 0000000..627388a
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diff --git a/calc-frontend/src/Animations/media/videos/limitsAnimation/480p15/partial_movie_files/Limit/partial_movie_file_list.txt b/calc-frontend/src/Animations/media/videos/limitsAnimation/480p15/partial_movie_files/Limit/partial_movie_file_list.txt
new file mode 100644
index 0000000..e07cda4
--- /dev/null
+++ b/calc-frontend/src/Animations/media/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-frontend/src/Animations/media/videos/limitsAnimation/480p15/partial_movie_files/Limit/1185818338_1240247844_223132457.mp4'
+file 'file:/home/drake/CalculusVisualizerProject/calc-visualizer/calc-frontend/src/Animations/media/videos/limitsAnimation/480p15/partial_movie_files/Limit/624642324_1376512726_2967433267.mp4'
+file 'file:/home/drake/CalculusVisualizerProject/calc-visualizer/calc-frontend/src/Animations/media/videos/limitsAnimation/480p15/partial_movie_files/Limit/624642324_4009246852_534934079.mp4'
+file 'file:/home/drake/CalculusVisualizerProject/calc-visualizer/calc-frontend/src/Animations/media/videos/limitsAnimation/480p15/partial_movie_files/Limit/624642324_2341082278_3212827279.mp4'
+file 'file:/home/drake/CalculusVisualizerProject/calc-visualizer/calc-frontend/src/Animations/media/videos/limitsAnimation/480p15/partial_movie_files/Limit/624642324_858855158_1247583088.mp4'
+file 'file:/home/drake/CalculusVisualizerProject/calc-visualizer/calc-frontend/src/Animations/media/videos/limitsAnimation/480p15/partial_movie_files/Limit/624642324_667144672_62268487.mp4'
diff --git a/calc-frontend/src/pages/Home.tsx b/calc-frontend/src/pages/Home.tsx
index c49a8e7..4f09c49 100644
--- a/calc-frontend/src/pages/Home.tsx
+++ b/calc-frontend/src/pages/Home.tsx
@@ -3,7 +3,9 @@ import { Link } from "react-router"
import { useAuth } from "../App/AuthContext";
import SignInButton from "../components/ui/SignInButton";
import SignOutButton from "../components/ui/SignOutButton";
-import derivativeVideo from '../Animations/media/videos/derivativeAnimation/480p15/DerivativeAnimation.mp4';
+import derivativeVideo from '../Animations/media/videos/derivativeAnimation/1080p60/DerivativeAnimation.mp4';
+import integralVideo from '../Animations/media/videos/integralAnimations/1080p60/RightRiemannSum.mp4';
+import limitVideo from '../Animations/media/videos/limitsAnimation/1080p60/Limit.mp4';
function Home() {
const { session, isPending } = useAuth();
@@ -85,7 +87,7 @@ function Home() {