用Octave计算函数极限（1）
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计算\(\displaystyle\lim_{n \to \infty}n(\frac{\pi}{2} - {\rm arctan}n)\)
程序代码如下
function [text_result, numeric_result] = func1(n_value)
    pkg load symbolic;
    n = sym('n');
    question = n * (pi / 2 - atan(n));
    lim = limit(question, n, n_value);
    text_result = ["\n", disp(lim)];
    numeric_result = eval(lim);
endfunction
令\(n \to \infty\)，计算结果如下
>> [text_result, numeric_result] = func1(inf)
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
    minus at line 47 column 5
    func1 at line 4 column 14

text_result =
    1

numeric_result = 1
令\(n \to 2\)，计算结果如下
>> [text_result, numeric_result] = func1(2)
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
minus at line 47 column 5
func1 at line 4 column 14

text_result =
  π - 2⋅atan(2)

numeric_result = 0.9273
可见符号解和数值解有可能不同。
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