import numpy as np
import matplotlib.pyplot as plt

定义 x 的范围

x = np.linspace(-5, 5, 400)

计算三个函数的值

y_cosh = np.cosh(x)
y_sinh = np.sinh(x)
y_half_exp = 0.5 * np.exp(x)

创建图形和坐标轴

plt.figure(figsize=(10, 6))
ax = plt.gca()

绘制函数

ax.plot(x, y_cosh, label=r'$y = \cosh(x)$', color='blue')
ax.plot(x, y_sinh, label=r'$y = \sinh(x)$', color='green')
ax.plot(x, y_half_exp, label=r'$y = \frac{1}{2}e^x$', color='red')

添加图例

plt.legend(loc='upper left')

添加网格

plt.grid(True)

设置标题和坐标轴标签

plt.title('Plot of $\cosh(x)$, $\sinh(x)$, and $\frac{1}{2}e^x$')
plt.xlabel('x')
plt.ylabel('y')

显示图形

plt.show()

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