exp（-x） - sinx = 0; _ MATLAB [英] exp(-x) - sinx = 0; _ MATLAB

问题描述

我打算到达这个功能的根源：



exp（-x） - sinx = 0 ;



这是我的代码：



------------ ------------------



x0 =输入（'请输入x0 :::'）;



eps =输入（'请输入步骤:::'）;



％eps是步骤



iterator = 0;



for i = 0：eps：x0



x = x + exp（-x） - sin（x）;



iterator = iteratio + 1;



结束



disp（'root :::'）;

disp（x） ;



disp（'iterate count :::'）;

disp（迭代器）;

< br $>
------------------------------



我不能使它工作。你可以帮我吗？

i'm planning to reach the root of this function:

exp(-x) - sinx = 0;

here is my code:

------------------------------

x0 = input('please enter x0 ::: ');

eps = input('please enter steps ::: ');

% eps is the step

iterator = 0;

for i=0:eps:x0

x=x+exp(-x) - sin(x);

iterator = iteratio + 1;

end

disp('root ::: ');
disp(x);

disp('iterate count ::: ');
disp(iterator);

------------------------------

well i can't make it work. can you help me with that?

推荐答案

我强烈建议首先得到图表的感觉。

1）sin（ x）周期性地在2⋅π并且每个n⋅π具有根（∀n∈N ₀ ）

2）sin（x）≈x（x远小于π/ 2）

3）e ^-x 将monotoinc变为零（∀x∈R，x≥0）

4）e < sup> -x 的样本值为：e ⁰ = 1，e ^-π≈0.0432，e ^-2⋅π ≈0.0019，e ^-3⋅π≈0.00008，e ^-4⋅π≈0.0000034，...



从这里，你可以假设e ^-x - sin（x）的根是

• ≈n⋅π（∀n∈N）（因为e ^-x 对于值x =π及以上可以忽略）
• ≈0.59（对于0和π之间的根） ）（通过设置e ^-x ≈x并估计并粗略计算π/ 6和π/ 4之间的某个值）

I strongly suggest to first get a "feeling" for the graph.
1) sin(x) is periodically in 2⋅π and has roots every n⋅π (∀ n ∈ Ν₀)
2) sin(x) ≈ x (x much smaller than π/2)
3) e^-x goes monotoinc to zero (∀ x ∈ R, x ≥ 0)
4) e^-x has sample values at: e⁰ = 1, e^-π ≈ 0.0432, e^-2⋅π ≈ 0.0019, e^-3⋅π ≈ 0.00008, e^-4⋅π ≈ 0.0000034, ...

From this, you can postulate that the roots for e^-x - sin(x) are

• ≈ n⋅π (∀ n ∈ Ν) (since e^-x for values x=π and above can be neglected)
• ≈ 0.59 (for the root between 0 and π) (found by setting e^-x ≈ x and estimating and roughly calculating some value between π/6 and π/4)

现在它正在工作，

Now it's working,

x0 = input('please enter x0 ::: ');
eps = input('please enter steps ::: ');
iterator = 0;
x=0;
iterator = 0;
for i=0:eps:x0
    x=x+exp(-x) - sin(x);
    iterator = iterator + 1;
end
disp('root ::: ');
disp(x);
disp('iterate count ::: ');
disp(iterator);

感谢所有人。

thanks to all.

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