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July 24, 2019 03:07
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2019 高考理科20题
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| from manimlib.imports import * | |
| class Playground(Scene): | |
| def construct(self): | |
| semicircle = Arc(fill_opacity=1, angle=PI/2) | |
| self.play(FadeIn(semicircle)) | |
| def Range(in_val,end_val,step=1): | |
| return list(np.arange(in_val,end_val+step,step)) | |
| class PlotGK1(GraphScene): | |
| CONFIG = { | |
| "y_max" : 1.5, | |
| "y_min" : -1.5, | |
| "x_max" : 10, | |
| "x_min" : -1, | |
| "y_tick_frequency" : 0.5, | |
| "x_tick_frequency" : 0.5, | |
| "graph_origin" : ORIGIN, | |
| "y_axis_label": None, # Don't write y axis label | |
| "x_axis_label": None, | |
| } | |
| def construct(self): | |
| self.setup_axes() | |
| plotf = self.get_graph(lambda x : np.sin(x) - np.log(x+1), | |
| color = GREEN, | |
| x_min=-0.8, | |
| x_max=8, | |
| ) | |
| plotdf = self.get_graph(lambda x : np.cos(x) - 1/(x+1), | |
| color = GRAY, | |
| x_min=-0.8, | |
| x_max=8, | |
| ) | |
| plotf.set_stroke(width=3) # width of line | |
| plotdf.set_stroke(width=2) | |
| # Animation | |
| e1 = TexMobject("f(x) = sin(x) - ln(1+x)").to_edge(LEFT) | |
| self.play(FadeIn(e1)) | |
| self.play(FadeOut(e1)) | |
| self.play(ShowCreation(plotf), run_time = 2) | |
| self.wait() | |
| e2 = TexMobject("f'(x) = cos(x) - \\frac{1}{1+x}").to_edge(LEFT) | |
| self.play(FadeIn(e2)) | |
| self.play(FadeOut(e2)) | |
| self.wait() | |
| self.play(ShowCreation(plotdf), run_time = 2) | |
| self.wait() | |
| # ------------------- play problem 1 | |
| e2 = TextMobject("(1) $f'(x)$ 在区间 $(-1, \\pi/2)$ \\\\ 中只有一个极值点").to_edge(LEFT) | |
| self.play(FadeIn(e2)) | |
| self.wait(3) | |
| self.play(FadeOut(e2)) | |
| # the first problem cares nothing about f(x) | |
| self.play(FadeOut(plotf)) | |
| # blines = self.get_vertical_line_to_graph(-1 , plotdf, | |
| # line_class=DashedLine) | |
| # self.play(ShowCreation(boundary_lines)) | |
| e4 = TextMobject("可以看出 $f'(x)$ 在区间内为凸").to_edge(LEFT).to_edge(UP) | |
| self.play(ShowCreation(e4)) | |
| self.wait(4) | |
| e5 = TextMobject("令 $g(x) = f'(x)$ ") | |
| e5.next_to(e4, DOWN) | |
| self.play(ShowCreation(e5)) | |
| e61 = TexMobject("g'(x) = -sin(x) + \\frac{1}{(1+x^2)}").to_edge(LEFT) | |
| e61.next_to(e5, DOWN) | |
| e62 = TexMobject("g''(x) = -cos(x) - \\frac{2x}{(1+x^2)^2} < 0 ").to_edge(LEFT) | |
| e62.next_to(e61, DOWN) | |
| self.play(ShowCreation(e61)) | |
| self.play(ShowCreation(e62)) | |
| self.wait(4) | |
| e7 = TextMobject("$g'(x) > 0 , -1<x<0$ \\\\ $g'(\\frac{\\pi}{2}) < 0$ ").to_edge(LEFT) | |
| e7.next_to(e62, DOWN) | |
| self.play(ShowCreation(e7)) | |
| e8 = TextMobject("证毕").to_edge(LEFT) | |
| e8.next_to(e7, DOWN) | |
| self.play(ShowCreation(e8)) | |
| def setup_axes(self): | |
| GraphScene.setup_axes(self) | |
| # width of edges | |
| self.x_axis.set_stroke(width=2) | |
| self.y_axis.set_stroke(width=2) | |
| # color of edges | |
| self.x_axis.set_color(RED) | |
| self.y_axis.set_color(YELLOW) | |
| # Add x,y labels | |
| func = TexMobject("y") | |
| var = TexMobject("x") | |
| func.set_color(BLUE) | |
| var.set_color(PURPLE) | |
| func.next_to(self.y_axis,UP) | |
| var.next_to(self.x_axis,RIGHT+UP) | |
| # Y labels | |
| self.y_axis.label_direction = LEFT*1.5 | |
| self.y_axis.add_numbers(*[-1,1]) | |
| #Parametters of x labels | |
| init_val_x = -1 | |
| step_x = 1 | |
| end_val_x = 5 | |
| # List of the positions of x labels | |
| values_decimal_x=Range(init_val_x,end_val_x,step_x) | |
| # List of tex objects | |
| list_x=TexMobject("-1", # -3pi/2 | |
| "0", # -pi | |
| "1", # -pi/2 | |
| "2", # 0 (space) | |
| "3", # pi/2 | |
| "4",# pi | |
| "5" # 3pi/2 | |
| ) | |
| #List touples (position,label) | |
| values_x = [(i,j) | |
| for i,j in zip(values_decimal_x,list_x) | |
| ] | |
| self.x_axis_labels = VGroup() | |
| for x_val, x_tex in values_x: | |
| x_tex.scale(0.7) | |
| if x_val == -PI or x_val == PI: #if x is equals -pi or pi | |
| x_tex.next_to(self.coords_to_point(x_val, 0), 2*DOWN) #Put 2*Down | |
| else: # In another case | |
| x_tex.next_to(self.coords_to_point(x_val, 0), DOWN) | |
| self.x_axis_labels.add(x_tex) | |
| self.play( | |
| *[Write(objeto) | |
| for objeto in [ | |
| self.y_axis, | |
| self.x_axis, | |
| self.x_axis_labels, | |
| func,var | |
| ] | |
| ], | |
| run_time=2 | |
| ) | |
| # 第二问 | |
| class PlotGK2(GraphScene): | |
| CONFIG = { | |
| "y_max" : 2, | |
| "y_min" : -2, | |
| "x_max" : 20, | |
| "x_min" : -1, | |
| "y_tick_frequency" : 0.5, | |
| "x_tick_frequency" : 0.5, | |
| "graph_origin" : ORIGIN, | |
| "y_axis_label": None, # Don't write y axis label | |
| "x_axis_label": None, | |
| } | |
| def construct(self): | |
| self.setup_axes() | |
| plotf = self.get_graph(lambda x : np.sin(x) - np.log(x+1), | |
| color = GREEN, | |
| x_min=-0.9, | |
| x_max=18, | |
| ) | |
| plotfup = self.get_graph(lambda x : 1 - np.log(x+1), | |
| color = GREEN, | |
| x_min=-0.9, | |
| x_max=18, | |
| ) | |
| plotdf = self.get_graph(lambda x : np.cos(x) - 1/(x+1), | |
| color = GRAY, | |
| x_min=-0.9, | |
| x_max=18, | |
| ) | |
| plotf.set_stroke(width=3) # width of line | |
| plotdf.set_stroke(width=2) | |
| # Animation | |
| e1 = TexMobject("f(x) = sin(x) - ln(1+x)").to_edge(LEFT) | |
| self.play(FadeIn(e1)) | |
| self.play(FadeOut(e1)) | |
| self.play(ShowCreation(plotf), run_time = 2) | |
| self.wait() | |
| e2 = TexMobject("f'(x) = cos(x) - \\frac{1}{1+x}").to_edge(LEFT) | |
| self.play(FadeIn(e2)) | |
| self.play(FadeOut(e2)) | |
| self.wait() | |
| self.play(ShowCreation(plotdf), run_time = 2) | |
| self.wait() | |
| # ------------------- play problem 1 | |
| e2 = TextMobject("(2) $f(x)$ 有且仅有两个零点 ").to_edge(LEFT) | |
| self.play(FadeIn(e2)) | |
| self.wait(4) | |
| self.play(FadeOut(e2)) | |
| # the first problem cares nothing about f(x) | |
| self.play(FadeOut(plotdf)) | |
| # blines = self.get_vertical_line_to_graph(-1 , plotdf, | |
| # line_class=DashedLine) | |
| # self.play(ShowCreation(boundary_lines)) | |
| e4 = TextMobject(" $-1 \le sin(x) \le 1$").to_edge(LEFT).to_edge(UP) | |
| self.play(ShowCreation(e4)) | |
| self.wait(4) | |
| e5 = TexMobject("f(x) \le 1 - ln(1+x)").to_edge(LEFT) | |
| e5.next_to(e4, DOWN) | |
| self.play(ShowCreation(e5), ShowCreationThenDestruction(plotfup)) | |
| e6 = TextMobject(" $x+1 > e$ 时， $f(x) < 0$ ").scale(0.6).to_edge(LEFT) | |
| e6.next_to(e5, DOWN) | |
| self.play(ShowCreation(e6)) | |
| e7 = TextMobject(" $x > e-1$ 时， $f(x) < 0$ ").scale(0.6).to_edge(LEFT) | |
| e7.next_to(e5, DOWN) | |
| vline = lambda x: DashedLine( | |
| self.coords_to_point(x, -10), | |
| self.coords_to_point(x, 10), | |
| stroke_width=2) | |
| vlinef = vline(np.e-1) | |
| vlinef.set_color(RED) | |
| self.play(Transform(e6, e7), ShowCreation(vlinef)) | |
| self.wait(4) | |
| e8 = TextMobject(" $f(\\frac{\\pi}{2}) = 1-ln(1+ \\frac{\\pi}{2}) >0$ ").scale(0.6).to_edge(LEFT) | |
| e8.next_to(e7, DOWN) | |
| vlinedf = vline(PI/2) | |
| vlinedf.set_color(YELLOW) | |
| self.play(ShowCreation(e8), ShowCreation(vlinedf)) | |
| self.wait(4) | |
| e9 = TextMobject(" $f(e-1) <0$ ").to_edge(LEFT) | |
| e9.next_to(e8, DOWN) | |
| e10 = TextMobject("又 $f'(x) < 0 x$ , \\\\ $f(x)$ 在 $(\\pi/2 , e-1)$ \\\\ 中仅有一个零点 ").scale(0.7).to_edge(LEFT) | |
| e10.next_to(e7, DOWN) | |
| self.play(FadeOut(e8) , Transform(e9, e10)) | |
| self.wait(4) | |
| e11 = TextMobject(" 易知 $f(x)$ 在 $(0, \\frac{\\pi}{2})$ 上先增后降").scale(0.5).to_edge(LEFT) | |
| e11.next_to(e10, DOWN) | |
| self.play( ShowCreation(e11)) | |
| e12= TextMobject(" $f(x) >0, x \in (0, \\frac{\\pi}{2})$ ").scale(0.5).to_edge(LEFT) | |
| e12.next_to(e11, DOWN) | |
| self.play( ShowCreation(e12)) | |
| self.wait(4) | |
| e13= TextMobject("又 $f(0) = 0$, \\\\ $f(x)$ 仅有两个零点 ").scale(0.5).to_edge(LEFT) | |
| e13.next_to(e12, DOWN) | |
| self.play( ShowCreation(e13)) | |
| e14= TextMobject(" 证毕 ").scale(0.5).to_edge(LEFT) | |
| e14.next_to(e13, DOWN) | |
| self.play( ShowCreation(e14)) | |
| self.wait(5) | |
| def setup_axes(self): | |
| GraphScene.setup_axes(self) | |
| # width of edges | |
| self.x_axis.set_stroke(width=2) | |
| self.y_axis.set_stroke(width=2) | |
| # color of edges | |
| self.x_axis.set_color(RED) | |
| self.y_axis.set_color(YELLOW) | |
| # Add x,y labels | |
| func = TexMobject("y") | |
| var = TexMobject("x") | |
| func.set_color(BLUE) | |
| var.set_color(PURPLE) | |
| func.next_to(self.y_axis,UP) | |
| var.next_to(self.x_axis,RIGHT+UP) | |
| # Y labels | |
| self.y_axis.label_direction = LEFT*1.5 | |
| self.y_axis.add_numbers(*[-1,1]) | |
| #Parametters of x labels | |
| init_val_x = -1 | |
| step_x = 1 | |
| end_val_x = 5 | |
| # List of the positions of x labels | |
| values_decimal_x=Range(init_val_x,end_val_x,step_x) | |
| # List of tex objects | |
| list_x=TexMobject("-1", # -3pi/2 | |
| "0", # -pi | |
| "1", # -pi/2 | |
| "2", # 0 (space) | |
| "3", # pi/2 | |
| "4",# pi | |
| "5" # 3pi/2 | |
| ) | |
| #List touples (position,label) | |
| values_x = [(i,j) | |
| for i,j in zip(values_decimal_x,list_x) | |
| ] | |
| self.x_axis_labels = VGroup() | |
| for x_val, x_tex in values_x: | |
| x_tex.scale(0.7) | |
| if x_val == -PI or x_val == PI: #if x is equals -pi or pi | |
| x_tex.next_to(self.coords_to_point(x_val, 0), 2*DOWN) #Put 2*Down | |
| else: # In another case | |
| x_tex.next_to(self.coords_to_point(x_val, 0), DOWN) | |
| self.x_axis_labels.add(x_tex) | |
| self.play( | |
| *[Write(objeto) | |
| for objeto in [ | |
| self.y_axis, | |
| self.x_axis, | |
| self.x_axis_labels, | |
| func,var | |
| ] | |
| ], | |
| run_time=2 | |
| ) | |
| class Last(GraphScene): | |
| def construct(self): | |
| e2 = TextMobject("谢谢观看") | |
| self.play(ShowCreationThenFadeOut(e2)) |
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