用Octave计算证明单调性(3)
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重要不等式(3) 当\(x \ne 0\)时,\({\rm e}^x \gt 1+x\)
计算\(\displaystyle\lim_{x \to 1}{\rm e}^x -1-x\)
程序代码如下
function [text_result, numeric_result] = func4(x_value)
pkg load symbolic;
x = sym('x');
question = exp(x) - 1 - x;
lim = limit(question, x, x_value);
text_result = ["\n", disp(lim)];
numeric_result = eval(lim);
endfunction
令\(x \to 1\),计算结果如下
>> [text_result, numeric_result] = func4(1)
text_result =
-2 + ℯ
numeric_result = 0.7183
令\(x \to -1\),计算结果如下
>> [text_result, numeric_result] = func4(-1)
text_result =
-1
ℯ
numeric_result = 0.3679