高数常用等价无穷小和泰勒公式动态图像

文章目录

• • • sinx~x
    • arcsinx~x
    • tanx~x
    • e^x-1~x
    • ln(x+1)~x
    • 1-cosx~1/2*x^2
    • sinx泰勒展开
    • arcsinx泰勒展开
    • tanx泰勒展开
    • arctanx泰勒展开
    • cosx泰勒展开
    • ln(x+1)泰勒展开
    • e^x泰勒展开
    • 1/(1-x)泰勒展开

下面的代码都是Maple，没有找到Maple就选择了Matlab代码

sinx~x

f := x;
g := sin(x);
plots[animatecurve]([f, g], x = -1 .. 1, color = [red, blue], legend = ["x", "sinx"], frames = 50);

arcsinx~x

f := x;
g := arcsin(x);
plots[animatecurve]([f, g], x = -1 .. 1, color = [red, blue], legend = ["x", arcsinx], frames = 50);

tanx~x

f := x;
g := tan(x);
plots[animatecurve]([f, g], x = -1 .. 1, color = [red, blue], legend = ["x", tanx], frames = 50);

e^x-1~x

f := x;
g := exp(x) - 1;
plots[animatecurve]([f, g], x = -1 .. 1, color = [red, blue], legend = ["x", exp(x) - 1], frames = 50);

ln(x+1)~x

f := x;
g := ln(x + 1);
plots[animatecurve]([f, g], x = -0.5 .. 0.5, color = [red, blue], legend = ["x", ln(x + 1)], frames = 50);

1-cosx~1/2*x^2

f := 1 - cos(x);
g := 1/2*x^2;
plots[animatecurve]([f, g], x = -1 .. 1, color = [red, blue], legend = [1 - cosx, 1/2*x^2], frames = 50);

sinx泰勒展开

f := x - 1/6*x^3;
g := sin(x);
plots[animatecurve]([f, g], x = -1.5 .. 1.5, color = [red, blue], legend = [x - 1/6*x^3, "sinx"], frames = 50);

arcsinx泰勒展开

f := x + 1/6*x^3;
g := arcsin(x);
plots[animatecurve]([f, g], x = -1 .. 1, color = [red, blue], legend = [x - 1/6*x^3, "arcsinx"], frames = 50);

tanx泰勒展开

f := x + 1/3*x^3;
g := tan(x);
plots[animatecurve]([f, g], x = -1 .. 1, color = [red, blue], legend = [x - 1/6*x^3, "tanx"], frames = 50);

arctanx泰勒展开

f := x - 1/3*x^3;
g := arctan(x);
plots[animatecurve]([f, g], x = -1 .. 1, color = [red, blue], legend = [x - 1/3*x^3, "arctanx"], frames = 50);

cosx泰勒展开

f := cos(x);
g := 1 - 1/2*x^2 + 1/24*x^4;
plots[animatecurve]([f, g], x = -2 .. 2, color = [red, blue], legend = [cosx, 1 - 1/2*x^2 + 1/24*x^4], frames = 50);

ln(x+1)泰勒展开

f := ln(1 + x);
g := x - 1/2*x^2 + 1/3*x^3 - 1/4*x^4;
plots[animatecurve]([f, g], x = -1 .. 1, color = [red, blue], legend = [ln(1 + x), x - 1/2*x^2 + 1/3*x^3 - 1/4*x^4], frames = 50);

e^x泰勒展开

f := exp(x);
g := 1 + x + x^2/2! + x^3/3!;
plots[animatecurve]([f, g], x = -1 .. 1, color = [red, blue], legend = [exp(x), 1 + x + x^2/2! + x^3/3!], frames = 50);

1/(1-x)泰勒展开

f := 1/(1 - x);
g := x^3 + x^2 + x + 1;
plots[animatecurve]([f, g], x = -0.5 .. 0.5, color = [red, blue], legend = [1/(1 - x), x^3 + x^2 + x + 1], frames = 50);