4.1双曲函数

曲线C{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="C" style="vertical-align:-6px;height:22px;width:14px" loading="lazy">有方程

y = 31 sinh x − 2 sinh 2x       x ∈ℝ{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Y空间等于31空间空间sinh空间空间x空间减去空间2空间空间sinh空间2空间空间空间空间空间空间空间空间空间空间空间空间空间x空间元素的实数" style="vertical-align:-6px;height:22px;width:264px" loading="lazy">

用自然对数来确定x{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="x" style="vertical-align:-6px;height:22px;width:11px" loading="lazy">静止点的坐标C{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="C" style="vertical-align:-6px;height:22px;width:14px" loading="lazy">．

tanh-1(x)=12 ln1+x1-x    –k < x < k{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Tanh的- 1次幂结束指数左括号x右括号等于1 / 2空间ln开括号分数分子1 + x /分母1 - x结束分数闭括号空间空间空间空间- k空间小于空间x斜体空间斜体小于斜体空间k" style="vertical-align:-17px;height:47px;width:287px" loading="lazy">

声明常量的值k.{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="k。" style="vertical-align:-6px;height:22px;width:16px" loading="lazy">

2x = tanh(ln2-3x){"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="2xspace等于tanh左括号ln√(2 - 3)√右括号" style="vertical-align:-6px;height:26px;width:165px" loading="lazy">