用Octave计算证明单调性（1）
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重要不等式（1） 当\(x \gt 0\)时，\({\rm ln}(1+x) \lt x\)
计算\(\displaystyle\lim_{n \to 0^+}{\rm ln}(1+x) - x\)
程序代码如下
function [text_result, numeric_result] = func2(x_value)
    pkg load symbolic;
    x = sym('x');
    question = log(1 + x) - x;
    lim = limit(question, x, x_value);
    text_result = ["\n", disp(lim)];
    numeric_result = eval(lim);
endfunction
令\(x \to 0^+\)，计算结果如下
>> [text_result, numeric_result] = func2(eps)
warning: passing floating-point values to sym is dangerous, see "help sym"
warning: called from
    double_to_sym_heuristic at line 50 column 7
    sym at line 384 column 13
    limit at line 92 column 5
    func2 at line 5 column 9

text_result =
         1              ⎛4503599627370497⎞
- ──────────────── + log⎜────────────────⎟
  4503599627370496      ⎝4503599627370496⎠

numeric_result = -2.4652e-32
令\(x \to -10\)，计算结果如下
>> [text_result, numeric_result] = func2(-10)
text_result =
    log(9) + 10 + ⅈ⋅π

numeric_result =  12.1972 +  3.1416i
可见，当\(x \lt 0\)时，\({\rm ln}(1+x)\)不小于\(x\)。
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