miaim 制作

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from manim import *


class SquareAndCircle(Scene):
    def construct(self):
        banner = ManimBanner() # 背景
        title = Title(f"Taylor ") # 不能用汉字
        self.add(title, banner)
        self.play(Create(title))
        self.wait()

        ex = MathTex(
            r"e^x = 1 + x + \frac{1}{2} x^2 + \frac{1}{6} x^3 + \cdots + \frac{1}{n!} x^n + \cdots,x\in(-\infty,+\infty)",
            substrings_to_isolate="x" # 只给x 上色
        )
        ex.set_color_by_tex("x", RED)
        ex.scale(0.8)
        self.add(ex)
        self.play(Write(ex))
        self.wait(3)
        ex.shift(UP)

        sinx = MathTex(
            r"\sin x = x - \frac{1}{3!} x^3 + \frac{1}{5!} x^5 + \cdots + (-1)^{n}\frac{1}{(2n-1)!} x^{2n-1} + \cdots,x\in(-1,+1)",
            substrings_to_isolate="x" # 只给x 上色
        )
        sinx.set_color_by_tex("x", GREEN)
        sinx.scale(0.8)
        self.add(sinx)
        self.play(Write(sinx))
        self.wait(3)
        groups=VGroup(ex, sinx) # 建立组
        groups.shift(UP)

        cosx = MathTex(
            r"\cos x = 1 - \frac{1}{2!} x^2 + \frac{1}{4!} x^4 + \cdots + (-1)^{n}\frac{1}{(2n)!} x^{2n} + \cdots,x\in(-1,+1)",
            substrings_to_isolate="x" # 只给x 上色
        )
        cosx.set_color_by_tex("x", BLUE)
        cosx.scale(0.8)
        self.add(cosx)
        self.play(Write(cosx))
        self.wait(3)
        groups.add(cosx) # 向组中添加元素 

        lnx = MathTex(
            r"\ln(x+1) = x - \frac{1}{2} x^2 + \frac{1}{3} x^3 + \cdots + (-1)^{n}\frac{1}{(n)!} x^{n} + \cdots,x\in(-1,+1)",
            substrings_to_isolate="x" # 只给x 上色
        )
        lnx.set_color_by_tex("x", PURPLE)
        lnx.scale(0.8)
        lnx.shift(DOWN)
        self.add(lnx)
        self.play(Write(lnx))
        self.wait(3)

        x_1 = MathTex(
            r"\frac{1}{1-x} =1 + x + x^2 + \cdots + x^n + \cdots,x\in(-1,+1)",
            substrings_to_isolate="x" # 只给x 上色
        )
        x_1.set_color_by_tex("x", PURPLE)
        x_1.scale(0.8)
        x_1.shift(DOWN*2)
        self.add(x_1)
        self.play(Write(x_1))
        self.wait(3)
  
        self.wait()