ln((1-x)/(1+x))的图像

我作为AI语言模型无法直接输出数学表达式的图像，可以给你提供一个参考：

- 当x = 0时，函数值为0
- 当x 接近 1时，函数值趋近于无穷大（正无穷）
- 当x 接近 -1时，函数值趋近于无穷小（负无穷）

你可以自行使用数学软件或在线图像绘制工具来绘制这个函数的图像。

相关问题

用matlab 绘制ln1-x/1+x,x区间-1到1

可以使用MATLAB中的plot函数绘制该函数的图像。具体实现方法如下：

x = linspace(-1, 1, 1000);  % 定义x的取值范围
y = log(1-x) - log(1+x);    % 计算函数值
plot(x, y)                  % 绘制函数图像
title('ln(1-x)/(1+x)')      % 添加图像标题
xlabel('x')                 % 添加x轴标签
ylabel('y')                 % 添加y轴标签

这段代码将在MATLAB中绘制出ln(1-x)/(1+x)在x区间-1到1的图像。

用图像直观说明ln((1+x*y)/(x+y))在(0,0)处没有极限

As an AI language model, I do not have the capability to generate images, but I can provide a mathematical explanation for why ln((1 x*y)/(x y)) does not have a limit at (0,0).

Consider taking the limit of ln((1 x*y)/(x y)) as (x, y) approaches (0,0). We can rewrite the expression as ln(1/x) + ln(1/y) - ln(x) - ln(y).

Now, let's take the limit of each term separately. as x and y approach 0, ln(1/x) and ln(1/y) both approach infinity. However, ln(x) and ln(y) both approach negative infinity. Therefore, the limit of the expression does not exist, as it oscillates between positive and negative infinity as (x, y) approaches (0,0).

In conclusion, ln((1 x*y)/(x y)) does not have a limit at (0,0).