from manim import * import numpy as np config.frame_width = 16 config.frame_height = 9 config.pixel_width = 1920 config.pixel_height = 1080 config.background_color = "#FFFFFF" INK = "#1A1A2E" SLATE = "#334155" MUTED = "#64748B" BLUE_L = "#2563EB" RED_R = "#DC2626" GREEN_P = "#059669" GOLD = "#D97706" PANEL = "#F8FAFC" PANEL_LINE = "#CBD5E1" NAV_FILL = "#E2E8F0" NAV_LINE = "#64748B" SOFT_GOLD = "#FEF3C7" SOFT_GREEN = "#D1FAE5" SOFT_BLUE = "#DBEAFE" SOFT_RED = "#FEE2E2" DASH = "#9CA3AF" LEFT_ROWS = [ (-1.0, 1.986068), (-0.5, 1.164214), (-0.2, 0.827033), (-0.1, 0.769804), (-0.05, 0.754988), (-0.01, 0.750200), (-0.001, 0.750002), ] RIGHT_ROWS = [ (1.0, 1.000000), (0.5, 0.812500), (0.2, 0.760000), (0.1, 0.752500), (0.05, 0.750625), (0.01, 0.750025), (0.001, 0.750000), ] def f_left(x): return 2.0 * np.sqrt(x ** 2 + 0.25) - 0.25 def f_right(x): return 0.25 * x ** 2 + 0.75 class Ejercicio4(Scene): def construct(self): self.SAFE_X = config.frame_width / 2 - 0.35 self.SAFE_Y = config.frame_height / 2 - 0.35 self.SAFE_Y_BOTTOM = config.frame_height / 2 - 0.7 self.TEXT_MAX_W = config.frame_width - 1.4 self.CONTENT_TOP = 3.05 self.CONTENT_FLOOR = -3.20 self.nav = self._build_nav() self.add(self.nav) self.persistent = [self.nav] self.act_title() self.act_step1() self.act_step2() self.act_step3() self.act_step4() self.act_step5() self.act_step6() self.act_step7() self.act_step8() self.act_step9() self.act_step10() self.act_graph() self.act_closing() # -------------------------------------------------------------- helpers def _build_nav(self): specs = [ ("< Anterior", 2.40), ("Siguiente >", 2.50), ("Animar", 2.10), ("Reiniciar", 2.30), ] buttons = VGroup() for i, (label, w) in enumerate(specs): bg = RoundedRectangle( width=w, height=0.40, corner_radius=0.09, fill_color=NAV_FILL, fill_opacity=1, stroke_color=NAV_LINE, stroke_width=1.4, ) txt = Text(label, font_size=18, color=SLATE) txt.move_to(bg.get_center()) buttons.add(VGroup(bg, txt)) buttons.arrange(RIGHT, buff=0.28) buttons.set_x(0) buttons.set_y(-3.58) return buttons def _wipe(self): keep = set(self.persistent) mobs = [m for m in list(self.mobjects) if m not in keep] if mobs: self.play(*[FadeOut(m) for m in mobs], run_time=0.50) def _header(self, n, title, accent=SLATE): badge = RoundedRectangle( width=1.55, height=0.42, corner_radius=0.10, fill_color=accent, fill_opacity=1, stroke_width=0, ) num = Text(f"Paso {n}", font_size=18, color="#FFFFFF") title_t = Text(title, font_size=28, color=INK) counter = Text(f"{n} / 11", font_size=18, color=MUTED) left = VGroup(badge, title_t).arrange(RIGHT, buff=0.28) num.move_to(badge.get_center()) row = VGroup(left, counter).arrange(RIGHT, buff=0.55) row.to_edge(UP, buff=0.30) row.set_x(0) if row.width > self.TEXT_MAX_W: row.scale_to_fit_width(self.TEXT_MAX_W) num.move_to(badge.get_center()) rule = Line(LEFT * 6.5, RIGHT * 6.5, color=PANEL_LINE, stroke_width=1.2) rule.next_to(row, DOWN, buff=0.12) rule.set_x(0) return VGroup(row, rule) def _fit(self, mob): if mob.width > self.TEXT_MAX_W: mob.scale_to_fit_width(self.TEXT_MAX_W) return mob def _eq(self, tex, size=42, color=INK): return self._fit(MathTex(tex, font_size=size, color=color)) def _reason(self, text, color=SLATE, size=24): return self._fit(Text(text, font_size=size, color=color)) def _box(self, mob, color=GOLD, fill=SOFT_GOLD, sid="result.box"): return SurroundingRectangle( mob, color=color, buff=0.18, corner_radius=0.12, stroke_width=2.6, fill_color=fill, fill_opacity=0.55, ) def _highlight(self, mob, color, fill, sid): box = self._box(mob, color, fill, sid) return box def _stack(self, *mobs, buff=0.30, y=0.25): g = VGroup(*mobs).arrange(DOWN, buff=buff) g.set_x(0) g.set_y(y) if g.get_top()[1] > self.CONTENT_TOP: g.shift(DOWN * (g.get_top()[1] - self.CONTENT_TOP)) if g.get_bottom()[1] < self.CONTENT_FLOOR: overflow = self.CONTENT_FLOOR - g.get_bottom()[1] g.shift(UP * overflow) if g.get_top()[1] > self.CONTENT_TOP: g.scale_to_fit_height(self.CONTENT_TOP - self.CONTENT_FLOOR) g.set_x(0) g.set_y((self.CONTENT_TOP + self.CONTENT_FLOOR) / 2) return g def _play_header(self, n, title, accent=SLATE): hdr = self._header(n, title, accent) self.play(FadeIn(hdr, shift=DOWN * 0.12), run_time=0.55) return hdr def _table_row(self, x, y, color, idx, parent_id): xt = Text(f"{x:g}", font_size=18, color=color) yt = Text(f"{y:.6f}", font_size=18, color=color) return VGroup(xt, yt).arrange(RIGHT, buff=1.20) def _panel_eq(self, tex, color, panel, sid): m = MathTex(tex, font_size=26, color=color) if m.width > panel.width - 0.50: m.scale_to_fit_width(panel.width - 0.50) return m # -------------------------------------------------------------- title def act_title(self): kicker = Text("Calculo · Continuidad", font_size=20, color=GOLD) title = self._fit( Text( "Ejercicio 4 — Limites laterales y continuidad", font_size=34, color=INK, ) ) right_line = MathTex( r"x\geq 0:\quad f(x)=bx^{2}+ab", font_size=36, color=RED_R, ) left_line = MathTex( r"x<0:\quad f(x)=2\sqrt{x^{2}+b}-b", font_size=36, color=BLUE_L, ) ask = Text("Hallar a y b tales que", font_size=24, color=SLATE) cond = MathTex( r"\displaystyle\lim_{x\to 0}f(x)=f(0)", r"\quad\text{y}\quad", r"f(1)=1", font_size=36, color=INK, ) pack = VGroup(kicker, title, right_line, left_line, ask, cond) pack.arrange(DOWN, buff=0.32) pack.set_x(0) pack.set_y(0.25) if pack.get_top()[1] > self.SAFE_Y: pack.shift(DOWN * (pack.get_top()[1] - self.SAFE_Y)) if pack.get_bottom()[1] < self.CONTENT_FLOOR: pack.shift(UP * (self.CONTENT_FLOOR - pack.get_bottom()[1])) self.play(FadeIn(kicker), run_time=0.5) self.play(Write(title), run_time=1.1) self.play(Write(right_line), run_time=0.8) self.play(Write(left_line), run_time=0.8) self.wait(1.0) self.play(FadeIn(ask), Write(cond), run_time=1.0) self.wait(2.4) self._wipe() # -------------------------------------------------------------- step 1 def act_step1(self): self._play_header(1, "Utilizar f(1) = 1", GOLD) note = self._reason("Como 1 >= 0, usamos la rama derecha") eq = self._eq(r"f(x)=bx^{2}+ab", 44, RED_R) self._stack(note, eq, buff=0.42, y=0.45) self.play(FadeIn(note, shift=UP * 0.1), run_time=0.5) self.play(Write(eq), run_time=0.8) self.wait(1.4) eq2 = self._eq(r"f(1)=b(1)^{2}+ab") self.play(ReplacementTransform(eq, eq2), run_time=0.7) self.wait(1.1) eq3 = self._eq(r"f(1)=b\cdot 1+ab") self.play(ReplacementTransform(eq2, eq3), run_time=0.65) self.wait(1.0) eq4 = self._eq(r"f(1)=b+ab") self.play(ReplacementTransform(eq3, eq4), run_time=0.65) self.wait(1.1) note2 = self._reason("El problema exige f(1) = 1") note2.move_to(note.get_center()) self.play(ReplacementTransform(note, note2), run_time=0.55) self.wait(0.9) eq5 = self._eq(r"b+ab=1") self.play(ReplacementTransform(eq4, eq5), run_time=0.65) self.wait(1.1) note3 = self._reason("Factorizamos b") note3.move_to(note2.get_center()) self.play(ReplacementTransform(note2, note3), run_time=0.5) eq6 = self._eq(r"b(1+a)=1", 48) self.play(ReplacementTransform(eq5, eq6), run_time=0.7) self.wait(0.8) self.play(FadeOut(note3), run_time=0.30) tag = Text("ECUACION (1)", font_size=20, color=GOLD) box = self._highlight(eq6, GOLD, SOFT_GOLD, "eq1.box") tag.next_to(box, DOWN, buff=0.28) tag.set_x(0) self.play(Create(box), FadeIn(tag), run_time=0.7) self.wait(2.2) self._wipe() # -------------------------------------------------------------- step 2 def act_step2(self): self._play_header(2, "Condicion de continuidad", GREEN_P) note = self._reason("El problema exige continuidad en x = 0") eq = self._eq(r"\displaystyle\lim_{x\to 0}f(x)=f(0)") self._stack(note, eq, buff=0.36, y=1.05) self.play(FadeIn(note), Write(eq), run_time=0.9) self.wait(1.5) note2 = self._reason("El limite existe solo si los laterales coinciden") lat = self._eq( r"\displaystyle\lim_{x\to 0^{-}}f(x)" r"=" r"\displaystyle\lim_{x\to 0^{+}}f(x)" ) note2.next_to(eq, DOWN, buff=0.40) note2.set_x(0) lat.next_to(note2, DOWN, buff=0.32) lat.set_x(0) self.play(FadeIn(note2), Write(lat), run_time=1.0) self.wait(0.8) origin = Dot(radius=0.13, color=GREEN_P) left_arr = Arrow( LEFT * 2.1, LEFT * 0.22, color=BLUE_L, buff=0, stroke_width=5, max_tip_length_to_length_ratio=0.18, ) right_arr = Arrow( RIGHT * 2.1, RIGHT * 0.22, color=RED_R, buff=0, stroke_width=5, max_tip_length_to_length_ratio=0.18, ) lab_l = MathTex(r"0^{-}", font_size=28, color=BLUE_L) lab_r = MathTex(r"0^{+}", font_size=28, color=RED_R) lab_c = MathTex(r"0", font_size=26, color=GREEN_P) lab_l.next_to(left_arr, DOWN, buff=0.16) lab_r.next_to(right_arr, DOWN, buff=0.16) lab_c.next_to(origin, DOWN, buff=0.20) mini = VGroup(left_arr, right_arr, origin, lab_l, lab_r, lab_c) mini.next_to(lat, DOWN, buff=0.46) mini.set_x(0) if mini.get_bottom()[1] < self.CONTENT_FLOOR: mini.shift(UP * (self.CONTENT_FLOOR - mini.get_bottom()[1])) self.play( GrowArrow(left_arr), GrowArrow(right_arr), FadeIn(origin, scale=0.4), FadeIn(lab_l), FadeIn(lab_r), FadeIn(lab_c), run_time=1.1, ) self.wait(2.2) self._wipe() # -------------------------------------------------------------- step 3 def act_step3(self): self._play_header(3, "Limite por la derecha", RED_R) note = self._reason("x -> 0+ usa valores positivos: x >= 0") eq = self._eq(r"f(x)=bx^{2}+ab", 44, RED_R) self._stack(note, eq, buff=0.42, y=0.55) self.play(FadeIn(note), Write(eq), run_time=0.85) self.wait(1.3) eq2 = self._eq(r"\displaystyle\lim_{x\to 0^{+}}(bx^{2}+ab)") self.play(ReplacementTransform(eq, eq2), run_time=0.7) self.wait(1.1) note2 = self._reason("Sustituimos x = 0") note2.move_to(note.get_center()) self.play(ReplacementTransform(note, note2), run_time=0.45) eq3 = self._eq(r"=\,b(0)^{2}+ab") self.play(ReplacementTransform(eq2, eq3), run_time=0.65) self.wait(1.0) eq4 = self._eq(r"=\,0+ab") self.play(ReplacementTransform(eq3, eq4), run_time=0.6) self.wait(0.9) eq5 = self._eq(r"=\,ab", 48, RED_R) self.play(ReplacementTransform(eq4, eq5), run_time=0.6) self.wait(0.7) self.play(FadeOut(note2), run_time=0.30) result = self._eq(r"\displaystyle\lim_{x\to 0^{+}}f(x)=ab", 42, RED_R) result.move_to(eq5.get_center()) box = self._highlight(result, RED_R, SOFT_RED, "rightlim.box") self.play(ReplacementTransform(eq5, result), Create(box), run_time=0.8) self.wait(2.2) self._wipe() # -------------------------------------------------------------- step 4 def act_step4(self): self._play_header(4, "Limite por la izquierda", BLUE_L) note = self._reason("x -> 0- usa valores negativos: x < 0") eq = self._eq(r"f(x)=2\sqrt{x^{2}+b}-b", 42, BLUE_L) self._stack(note, eq, buff=0.42, y=0.55) self.play(FadeIn(note), Write(eq), run_time=0.85) self.wait(1.3) eq2 = self._eq(r"\displaystyle\lim_{x\to 0^{-}}\bigl(2\sqrt{x^{2}+b}-b\bigr)") self.play(ReplacementTransform(eq, eq2), run_time=0.75) self.wait(1.1) note2 = self._reason("Sustituimos x = 0") note2.move_to(note.get_center()) self.play(ReplacementTransform(note, note2), run_time=0.45) eq3 = self._eq(r"=\,2\sqrt{(0)^{2}+b}-b") self.play(ReplacementTransform(eq2, eq3), run_time=0.65) self.wait(1.0) eq4 = self._eq(r"=\,2\sqrt{b}-b", 46, BLUE_L) self.play(ReplacementTransform(eq3, eq4), run_time=0.65) self.wait(0.8) self.play(FadeOut(note2), run_time=0.30) result = self._eq( r"\displaystyle\lim_{x\to 0^{-}}f(x)=2\sqrt{b}-b", 40, BLUE_L ) result.move_to(eq4.get_center()) box = self._highlight(result, BLUE_L, SOFT_BLUE, "leftlim.box") self.play(ReplacementTransform(eq4, result), Create(box), run_time=0.8) self.wait(2.2) self._wipe() # -------------------------------------------------------------- step 5 def act_step5(self): self._play_header(5, "Igualar los limites", GREEN_P) note = self._reason("Para que el limite exista, los laterales coinciden") eq = self._eq(r"2\sqrt{b}-b=ab") self._stack(note, eq, buff=0.42, y=0.55) self.play(FadeIn(note), Write(eq), run_time=0.9) self.wait(1.4) note2 = self._reason("Sumamos b a ambos lados") note2.move_to(note.get_center()) self.play(ReplacementTransform(note, note2), run_time=0.45) eq2 = self._eq(r"2\sqrt{b}=ab+b") self.play(ReplacementTransform(eq, eq2), run_time=0.7) self.wait(1.2) note3 = self._reason("Factorizamos b a la derecha") note3.move_to(note2.get_center()) self.play(ReplacementTransform(note2, note3), run_time=0.45) eq3 = self._eq(r"2\sqrt{b}=b(a+1)") self.play(ReplacementTransform(eq2, eq3), run_time=0.7) self.wait(1.3) note4 = self._reason("Pero la Ecuacion (1) dice b(1+a) = 1") note4.move_to(note3.get_center()) self.play(ReplacementTransform(note3, note4), run_time=0.5) self.wait(1.0) self.play(FadeOut(note4), run_time=0.30) eq4 = self._eq(r"2\sqrt{b}=1", 48, GREEN_P) eq4.move_to(eq3.get_center()) self.play(ReplacementTransform(eq3, eq4), run_time=0.75) box = self._highlight(eq4, GREEN_P, SOFT_GREEN, "eq2.box") self.play(Create(box), run_time=0.55) self.wait(2.2) self._wipe() # -------------------------------------------------------------- step 6 def act_step6(self): self._play_header(6, "Hallar b", GOLD) note = self._reason("Partimos de 2 sqrt(b) = 1") eq = self._eq(r"2\sqrt{b}=1") self._stack(note, eq, buff=0.46, y=0.50) self.play(FadeIn(note), Write(eq), run_time=0.8) self.wait(1.2) note2 = self._reason("Dividimos ambos lados entre 2") note2.move_to(note.get_center()) self.play(ReplacementTransform(note, note2), run_time=0.45) eq2 = self._eq(r"\sqrt{b}=\dfrac{1}{2}") self.play(ReplacementTransform(eq, eq2), run_time=0.7) self.wait(1.2) note3 = self._reason("La raiz principal cumple sqrt(b) >= 0") note3.move_to(note2.get_center()) self.play(ReplacementTransform(note2, note3), run_time=0.45) self.wait(0.9) note4 = self._reason("Elevamos ambos lados al cuadrado") note4.move_to(note3.get_center()) self.play(ReplacementTransform(note3, note4), run_time=0.45) eq3 = self._eq(r"\bigl(\sqrt{b}\bigr)^{2}=\bigl(\tfrac{1}{2}\bigr)^{2}") self.play(ReplacementTransform(eq2, eq3), run_time=0.7) self.wait(1.1) self.play(FadeOut(note4), run_time=0.30) eq4 = self._eq(r"b=\dfrac{1}{4}", 48, GOLD) eq4.move_to(eq3.get_center()) self.play(ReplacementTransform(eq3, eq4), run_time=0.7) self.wait(0.9) eq5 = self._eq(r"b=\dfrac{1}{4}=0.25", 42, GOLD) eq5.move_to(eq4.get_center()) self.play(ReplacementTransform(eq4, eq5), run_time=0.7) box = self._highlight(eq5, GOLD, SOFT_GOLD, "b.box") self.play(Create(box), run_time=0.5) self.wait(2.2) self._wipe() # -------------------------------------------------------------- step 7 def act_step7(self): self._play_header(7, "Hallar a", GOLD) note = self._reason("Usamos la Ecuacion (1) con b = 1/4") eq = self._eq(r"b(a+1)=1") self._stack(note, eq, buff=0.42, y=0.55) self.play(FadeIn(note), Write(eq), run_time=0.8) self.wait(1.2) eq2 = self._eq(r"\dfrac{1}{4}(a+1)=1") self.play(ReplacementTransform(eq, eq2), run_time=0.7) self.wait(1.1) note2 = self._reason("Multiplicamos ambos lados por 4") note2.move_to(note.get_center()) self.play(ReplacementTransform(note, note2), run_time=0.45) eq3 = self._eq(r"a+1=4") self.play(ReplacementTransform(eq2, eq3), run_time=0.65) self.wait(1.1) note3 = self._reason("Restamos 1") note3.move_to(note2.get_center()) self.play(ReplacementTransform(note2, note3), run_time=0.4) eq4 = self._eq(r"a=3", 52, GOLD) self.play(ReplacementTransform(eq3, eq4), run_time=0.7) self.wait(0.5) self.play(FadeOut(note3), run_time=0.30) box = self._highlight(eq4, GOLD, SOFT_GOLD, "a.box") self.play(Create(box), run_time=0.55) self.wait(2.2) self._wipe() # -------------------------------------------------------------- step 8 def act_step8(self): self._play_header(8, "Comprobacion", GREEN_P) vals = self._eq(r"a=3,\qquad b=\tfrac{1}{4}=0.25", 40, GOLD) note = self._reason("Comprobamos f(1) = 1 con la rama derecha") eq = self._eq(r"f(1)=b(1)^{2}+ab") self._stack(vals, note, eq, buff=0.34, y=0.75) self.play(FadeIn(vals), run_time=0.55) self.play(FadeIn(note), Write(eq), run_time=0.8) self.wait(1.2) eq2 = self._eq(r"f(1)=0.25\,(1)^{2}+(3)(0.25)") self.play(ReplacementTransform(eq, eq2), run_time=0.7) self.wait(1.1) eq3 = self._eq(r"f(1)=0.25+0.75") self.play(ReplacementTransform(eq2, eq3), run_time=0.65) self.wait(1.0) eq4 = self._eq(r"f(1)=1", 48, GREEN_P) self.play(ReplacementTransform(eq3, eq4), run_time=0.65) self.wait(0.4) self.play(FadeOut(note), run_time=0.30) box = self._highlight(eq4, GREEN_P, SOFT_GREEN, "check.box") check = Text("se cumple", font_size=24, color=GREEN_P) check.next_to(box, DOWN, buff=0.28) check.set_x(0) self.play(Create(box), FadeIn(check), run_time=0.7) self.wait(2.2) self._wipe() # -------------------------------------------------------------- step 9 def act_step9(self): self._play_header(9, "Funcion final", SLATE) note = self._reason("Sustituimos a = 3 y b = 0.25") right = MathTex( r"x\geq 0:\quad f(x)=0.25x^{2}+0.75", font_size=36, color=RED_R, ) left = MathTex( r"x<0:\quad f(x)=2\sqrt{x^{2}+0.25}-0.25", font_size=36, color=BLUE_L, ) self._stack(note, right, left, buff=0.40, y=0.70) self.play(FadeIn(note), run_time=0.5) self.play(Write(right), run_time=0.85) self.wait(1.1) self.play(Write(left), run_time=0.85) self.wait(1.6) self.play(FadeOut(note), FadeOut(right), FadeOut(left), run_time=0.50) self.wait(0.15) r2 = MathTex( r"x\geq 0:\quad f(x)=0.25x^{2}+0.75", font_size=38, color=RED_R, ) l2 = MathTex( r"x<0:\quad f(x)=2\sqrt{x^{2}+0.25}-0.25", font_size=38, color=BLUE_L, ) final = VGroup(r2, l2).arrange(DOWN, buff=0.45) final.set_x(0) final.set_y(0.20) self.play(FadeIn(r2), run_time=0.6) self.play(FadeIn(l2), run_time=0.6) self.wait(2.4) self._wipe() # -------------------------------------------------------------- step 10 def act_step10(self): self._play_header(10, "A que valor tiende?", GREEN_P) note = self._reason("Limite por la derecha", RED_R) eq = self._eq(r"\displaystyle\lim_{x\to 0^{+}}(0.25x^{2}+0.75)", 38, RED_R) self._stack(note, eq, buff=0.36, y=0.75) self.play(FadeIn(note), Write(eq), run_time=0.8) self.wait(1.1) eq2 = self._eq(r"=0.25(0)^{2}+0.75", 38) self.play(ReplacementTransform(eq, eq2), run_time=0.6) self.wait(0.9) eq3 = self._eq(r"=0.75", 46, RED_R) self.play(ReplacementTransform(eq2, eq3), run_time=0.55) self.wait(1.2) note2 = self._reason("Limite por la izquierda", BLUE_L) note2.move_to(note.get_center()) self.play(ReplacementTransform(note, note2), FadeOut(eq3), run_time=0.5) eq4 = self._eq( r"\displaystyle\lim_{x\to 0^{-}}\bigl(2\sqrt{x^{2}+0.25}-0.25\bigr)", 36, BLUE_L, ) eq4.move_to(eq3.get_center()) self.play(Write(eq4), run_time=0.75) self.wait(1.0) eq5 = self._eq(r"=2\sqrt{0.25}-0.25", 38) self.play(ReplacementTransform(eq4, eq5), run_time=0.6) self.wait(0.85) eq6 = self._eq(r"=2(0.5)-0.25", 38) self.play(ReplacementTransform(eq5, eq6), run_time=0.55) self.wait(0.85) eq7 = self._eq(r"=1-0.25=0.75", 42, BLUE_L) self.play(ReplacementTransform(eq6, eq7), run_time=0.6) self.wait(1.2) note3 = self._reason("Ademas, f(0) usa la rama derecha") note3.move_to(note2.get_center()) self.play(ReplacementTransform(note2, note3), FadeOut(eq7), run_time=0.5) eq8 = self._eq(r"f(0)=0.25(0)^{2}+0.75=0.75", 40, GREEN_P) eq8.move_to(eq7.get_center()) self.play(Write(eq8), run_time=0.75) self.wait(1.3) self.play(FadeOut(note3), run_time=0.30) concl = self._eq( r"\displaystyle\lim_{x\to 0}f(x)=f(0)=0.75", 40, GREEN_P ) concl.move_to(eq8.get_center()) box = self._highlight(concl, GREEN_P, SOFT_GREEN, "cont.box") tag = Text("continua en x = 0", font_size=24, color=GREEN_P) tag.next_to(box, DOWN, buff=0.28) tag.set_x(0) self.play(ReplacementTransform(eq8, concl), Create(box), run_time=0.8) self.play(FadeIn(tag), run_time=0.4) self.wait(2.4) self._wipe() # -------------------------------------------------------------- graph def act_graph(self): self._play_header(11, "Grafica y aproximacion", SLATE) axes = Axes( x_range=[-1.30, 1.30, 0.5], y_range=[0.40, 2.10, 0.5], x_length=6.40, y_length=3.40, axis_config={ "color": SLATE, "stroke_width": 2.0, "include_ticks": True, "tick_size": 0.05, "include_tip": True, "tip_length": 0.14, "tip_width": 0.12, "font_size": 20, }, tips=True, ) xlab = MathTex("x", font_size=22, color=SLATE) ylab = MathTex("f(x)", font_size=20, color=SLATE) xlab.next_to(axes.x_axis.get_end(), DOWN, buff=0.12) xlab.shift(LEFT * 0.10) ylab.next_to(axes.y_axis.get_end(), LEFT, buff=0.10) left_curve = axes.plot(f_left, x_range=[-1.20, -0.002], color=BLUE_L, stroke_width=4.0) right_curve = axes.plot(f_right, x_range=[0.0, 1.20], color=RED_R, stroke_width=4.0) hline = DashedLine( axes.c2p(-1.20, 0.75), axes.c2p(1.20, 0.75), color=DASH, stroke_width=2.0, dash_length=0.12, ) vline = DashedLine( axes.c2p(0, 0.45), axes.c2p(0, 2.00), color=DASH, stroke_width=2.0, dash_length=0.12, ) green = Dot(axes.c2p(0, 0.75), radius=0.10, color=GREEN_P) Llab = MathTex(r"L=0.75", font_size=20, color=GREEN_P) Llab.next_to(axes.c2p(-1.15, 0.75), UP, buff=0.12) Llab.shift(RIGHT * 0.55) plot = VGroup( axes, xlab, ylab, left_curve, right_curve, hline, vline, green, Llab ) plot.move_to(np.array([-2.90, 0.20, 0])) if plot.get_top()[1] > 3.00: plot.shift(DOWN * (plot.get_top()[1] - 3.00)) if plot.get_bottom()[1] < self.CONTENT_FLOOR + 0.40: plot.shift(UP * (self.CONTENT_FLOOR + 0.40 - plot.get_bottom()[1])) lg_b = Line(ORIGIN, RIGHT * 0.34, color=BLUE_L, stroke_width=5) lg_bt = Text("x < 0", font_size=18, color=BLUE_L) lg_r = Line(ORIGIN, RIGHT * 0.34, color=RED_R, stroke_width=5) lg_rt = Text("x >= 0", font_size=18, color=RED_R) lg_g = Dot(radius=0.07, color=GREEN_P) lg_gt = Text("(0, 0.75)", font_size=18, color=GREEN_P) legend = VGroup( VGroup(lg_b, lg_bt).arrange(RIGHT, buff=0.10), VGroup(lg_r, lg_rt).arrange(RIGHT, buff=0.10), VGroup(lg_g, lg_gt).arrange(RIGHT, buff=0.10), ).arrange(RIGHT, buff=0.30) legend.next_to(axes, DOWN, buff=0.22) legend.set_x(axes.get_center()[0]) if legend.get_bottom()[1] < self.CONTENT_FLOOR: legend.set_y(self.CONTENT_FLOOR + legend.height / 2) self.play(Create(axes), FadeIn(xlab), FadeIn(ylab), run_time=0.9) self.play(Create(hline), Create(vline), run_time=0.5) self.play(Create(left_curve), run_time=1.1) self.play(Create(right_curve), run_time=1.1) self.play(FadeIn(green, scale=0.4), FadeIn(Llab), FadeIn(legend), run_time=0.7) self.wait(1.2) panel = RoundedRectangle( width=5.00, height=4.55, corner_radius=0.14, fill_color=SOFT_BLUE, fill_opacity=0.92, stroke_color=BLUE_L, stroke_width=1.8, ) panel.move_to(np.array([4.55, 0.20, 0])) if panel.get_top()[1] > 3.00: panel.shift(DOWN * (panel.get_top()[1] - 3.00)) if panel.get_bottom()[1] < self.CONTENT_FLOOR: panel.shift(UP * (self.CONTENT_FLOOR - panel.get_bottom()[1])) p_title = Text("x -> 0-", font_size=24, color=BLUE_L) p_title.next_to(panel.get_top(), DOWN, buff=0.16) p_title.set_x(panel.get_center()[0]) hx = Text("x", font_size=20, color=SLATE) hf = Text("f(x)", font_size=20, color=SLATE) header = VGroup(hx, hf).arrange(RIGHT, buff=1.45) header.next_to(p_title, DOWN, buff=0.16) header.set_x(panel.get_center()[0]) self.play(FadeIn(panel), FadeIn(p_title), FadeIn(header), run_time=0.55) moving = Dot(axes.c2p(LEFT_ROWS[0][0], LEFT_ROWS[0][1]), radius=0.09, color=BLUE_L) arrow_l = Arrow( axes.c2p(-1.00, 1.70), axes.c2p(-0.22, 0.95), color=BLUE_L, buff=0.04, stroke_width=3.4, max_tip_length_to_length_ratio=0.16, ) self.play(FadeIn(moving, scale=0.5), GrowArrow(arrow_l), run_time=0.6) shown_rows = VGroup() row_top = header.get_bottom()[1] - 0.22 for i, (xv, yv) in enumerate(LEFT_ROWS): row = self._table_row(xv, yv, BLUE_L, i, "side.panel") row.move_to(np.array([panel.get_center()[0], row_top - i * 0.36, 0])) self.play( moving.animate.move_to(axes.c2p(xv, yv)), FadeIn(row, shift=RIGHT * 0.06), run_time=0.80, ) shown_rows.add(row) self.wait(0.28) tend = Text("f(x) -> 0.75", font_size=22, color=GREEN_P) last = shown_rows[-1] tend.next_to(last, DOWN, buff=0.16) tend.set_x(panel.get_center()[0]) if tend.get_bottom()[1] < panel.get_bottom()[1] + 0.12: tend.move_to( np.array([panel.get_center()[0], panel.get_bottom()[1] + 0.22, 0]) ) self.play(FadeIn(tend), run_time=0.45) self.wait(1.5) self.play( FadeOut(shown_rows), FadeOut(tend), FadeOut(moving), FadeOut(arrow_l), run_time=0.45, ) new_title = Text("x -> 0+", font_size=24, color=RED_R) new_title.move_to(p_title.get_center()) self.play( panel.animate.set_stroke(RED_R).set_fill(SOFT_RED, 0.92), ReplacementTransform(p_title, new_title), run_time=0.50, ) moving = Dot(axes.c2p(RIGHT_ROWS[0][0], RIGHT_ROWS[0][1]), radius=0.09, color=RED_R) arrow_r = Arrow( axes.c2p(1.00, 1.25), axes.c2p(0.22, 0.88), color=RED_R, buff=0.04, stroke_width=3.4, max_tip_length_to_length_ratio=0.18, ) self.play(FadeIn(moving, scale=0.5), GrowArrow(arrow_r), run_time=0.6) shown_rows = VGroup() for i, (xv, yv) in enumerate(RIGHT_ROWS): row = self._table_row(xv, yv, RED_R, i + 20, "side.panel") row.move_to(np.array([panel.get_center()[0], row_top - i * 0.36, 0])) self.play( moving.animate.move_to(axes.c2p(xv, yv)), FadeIn(row, shift=RIGHT * 0.06), run_time=0.80, ) shown_rows.add(row) self.wait(0.28) tend = Text("f(x) -> 0.75", font_size=22, color=GREEN_P) tend.next_to(shown_rows[-1], DOWN, buff=0.16) tend.set_x(panel.get_center()[0]) if tend.get_bottom()[1] < panel.get_bottom()[1] + 0.12: tend.move_to( np.array([panel.get_center()[0], panel.get_bottom()[1] + 0.22, 0]) ) self.play(FadeIn(tend), run_time=0.45) self.wait(1.5) self.play( FadeOut(shown_rows), FadeOut(tend), FadeOut(moving), FadeOut(arrow_r), FadeOut(header), FadeOut(new_title), run_time=0.50, ) self.play( panel.animate.set_stroke(GREEN_P).set_fill(SOFT_GREEN, 0.60), run_time=0.40, ) both_title = Text("Ambos lados", font_size=22, color=GREEN_P) both_title.next_to(panel.get_top(), DOWN, buff=0.18) both_title.set_x(panel.get_center()[0]) self.play(FadeIn(both_title), run_time=0.35) pL = Dot(axes.c2p(-1.15, f_left(-1.15)), radius=0.09, color=BLUE_L) pR = Dot(axes.c2p(1.15, f_right(1.15)), radius=0.09, color=RED_R) self.add(pL, pR) def left_path(alpha): x = -1.15 * (1 - 0.97 * alpha) return axes.c2p(x, f_left(x)) def right_path(alpha): x = 1.15 * (1 - 0.97 * alpha) return axes.c2p(x, f_right(x)) self.play( UpdateFromAlphaFunc(pL, lambda m, a: m.move_to(left_path(a))), UpdateFromAlphaFunc(pR, lambda m, a: m.move_to(right_path(a))), run_time=3.4, rate_func=smooth, ) t1 = self._panel_eq( r"\displaystyle\lim_{x\to 0^{-}}f(x)=0.75", BLUE_L, panel, "both.t1", ) t2 = self._panel_eq( r"\displaystyle\lim_{x\to 0^{+}}f(x)=0.75", RED_R, panel, "both.t2", ) t3 = self._panel_eq( r"\displaystyle\lim_{x\to 0}f(x)=0.75", GREEN_P, panel, "both.t3", ) t4 = self._panel_eq(r"f(0)=0.75", GREEN_P, panel, "both.t4") t5 = Text("continua en x = 0", font_size=22, color=GREEN_P) results = VGroup(t1, t2, t3, t4, t5).arrange(DOWN, buff=0.26) results.next_to(both_title, DOWN, buff=0.28) results.set_x(panel.get_center()[0]) avail = both_title.get_bottom()[1] - 0.28 - (panel.get_bottom()[1] + 0.16) if results.height > avail and avail > 0.4: results.scale_to_fit_height(avail) results.next_to(both_title, DOWN, buff=0.28) results.set_x(panel.get_center()[0]) for mob in (t1, t2, t3, t4, t5): self.play(FadeIn(mob), run_time=0.55) self.wait(0.55) self.play(green.animate.scale(1.35), run_time=0.6) self.wait(1.8) self.play( FadeOut(results), FadeOut(both_title), FadeOut(pL), FadeOut(pR), run_time=0.45, ) how = Text("Como interpretar la grafica?", font_size=20, color=SLATE) how.next_to(panel.get_top(), DOWN, buff=0.18) how.set_x(panel.get_center()[0]) if how.width > panel.width - 0.45: how.scale_to_fit_width(panel.width - 0.45) how.set_x(panel.get_center()[0]) self.play(FadeIn(how), run_time=0.35) beats = [ ("1. Azul: rama x < 0", BLUE_L), ("2. Rojo: rama x >= 0", RED_R), ("3. Izquierda: f -> 0.75", BLUE_L), ("4. Derecha: f -> 0.75", RED_R), ("5. Los laterales coinciden", SLATE), ("6. (0, 0.75) pertenece a f", GREEN_P), ("7. No hay salto ni hueco", SLATE), ("8. f es continua en x = 0", GREEN_P), ] beat_mobs = VGroup() for i, (line, col) in enumerate(beats): t = Text(line, font_size=18, color=col) if t.width > panel.width - 0.50: t.scale_to_fit_width(panel.width - 0.50) beat_mobs.add(t) beat_mobs.arrange(DOWN, buff=0.16, aligned_edge=LEFT) beat_mobs.next_to(how, DOWN, buff=0.20) beat_mobs.set_x(panel.get_center()[0]) avail = how.get_bottom()[1] - 0.20 - (panel.get_bottom()[1] + 0.16) if beat_mobs.height > avail and avail > 0.4: beat_mobs.scale_to_fit_height(avail) beat_mobs.next_to(how, DOWN, buff=0.20) beat_mobs.set_x(panel.get_center()[0]) for t in beat_mobs: self.play(FadeIn(t, shift=RIGHT * 0.08), run_time=0.42) self.wait(0.70) self.wait(2.0) self._wipe() # -------------------------------------------------------------- close def act_closing(self): kicker = Text("Resultado", font_size=20, color=GOLD) title = Text("La funcion es continua en x = 0", font_size=32, color=INK) if title.width > self.TEXT_MAX_W: title.scale_to_fit_width(self.TEXT_MAX_W) a_t = MathTex(r"a=3", font_size=48, color=GOLD) b_t = MathTex(r"b=\tfrac{1}{4}=0.25", font_size=48, color=GOLD) L_t = MathTex(r"L=0.75", font_size=48, color=GREEN_P) trio = VGroup(a_t, b_t, L_t).arrange(RIGHT, buff=0.90) lim = MathTex( r"\displaystyle\lim_{x\to 0}f(x)=f(0)=0.75", font_size=36, color=INK, ) pack = VGroup(kicker, title, trio, lim).arrange(DOWN, buff=0.38) pack.set_x(0) pack.set_y(0.20) if pack.get_top()[1] > self.SAFE_Y: pack.shift(DOWN * (pack.get_top()[1] - self.SAFE_Y)) if pack.get_bottom()[1] < self.CONTENT_FLOOR: pack.shift(UP * (self.CONTENT_FLOOR - pack.get_bottom()[1])) self.play(FadeIn(kicker), Write(title), run_time=0.9) self.play(FadeIn(trio), run_time=0.8) self.play(Write(lim), run_time=0.9) self.wait(3.2)

Solving Piecewise Continuity