lab7

python/laborator/lab7.py

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+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Fri Apr  3 14:08:00 2026
+
+@author: alex
+"""
+import numpy as np
+import matplotlib.pyplot as plt
+
+# 1
+
+x = np.linspace(-3,3,100)
+f_x = x**3 - 3*x
+
+plt.title("$f(x)=x^3-3x$")
+plt.xlabel("$x$")
+plt.ylabel("$y$")
+plt.grid(True)
+plt.plot(x,f_x,label="$x^3 - 3x$")
+
+plt.legend()
+plt.axhline(0, color="black", linewidth=0.8)
+plt.axvline(0, color="black", linewidth=0.8)
+plt.show()
+
+#2
+
+x_g_h = np.linspace(-2,2,100)
+g_x = np.exp(x_g_h)
+h_x = np.exp(-x_g_h)
+
+plt.title("$e^x$ si $e^{-x}$")
+plt.xlabel("$x$")
+plt.ylabel("$y$")
+plt.plot(x_g_h, g_x, label = "$e^x$")
+plt.plot(x_g_h, h_x, label ="$e^{-x}$")
+plt.scatter(0,1, s = 20, label="intersecție")
+
+plt.legend()
+plt.axhline(0, color="black", linewidth=0.8)
+plt.axvline(0, color="black", linewidth=0.8)
+plt.show()
+
+#3
+
+x_trig = np.linspace(0, 2*np.pi, 600)
+sin_x = np.sin(x_trig)
+sin_2x = np.sin(2*x_trig)
+sin_3x = np.sin(3*x_trig)
+
+plt.title("$sin(x)$ $sin(2x)$ $sin(3x)$")
+plt.xlabel("$x$")
+plt.ylabel("$y$")
+plt.plot(x_trig, sin_x, label = "$sin(x)$")
+plt.plot(x_trig, sin_2x, label = "$sin(2x)$")
+plt.plot(x_trig, sin_3x, label = "$sin(3x)$")
+
+plt.legend()
+plt.axhline(0, color="black", linewidth=0.8)
+plt.axvline(0, color="black", linewidth=0.8)
+plt.show()
+
+#4
+
+x = np.linspace(-10,10,10)
+y_1 = x - 2
+y_2 = x
+y_3 = x + 2 
+y_4 = x + 4
+
+plt.title("Funcții liniare1")
+plt.xlabel("$x$")
+plt.ylabel("$y$")
+
+plt.plot(x, y_1, label = "$x - 2$")
+plt.plot(x, y_2, label = "$x$")
+plt.plot(x, y_3, label = "$x+2$")
+plt.plot(x, y_4, label = "$x+4$")
+# dreptele au aceeasi panta
+# nu se intersecteaza
+# termenul liber e distanta fata de dreapta y = x
+
+plt.legend()
+plt.axhline(0, color="black", linewidth=0.8)
+plt.axvline(0, color="black", linewidth=0.8)
+plt.show()
+
+#5
+
+x = np.linspace(-4,4,100)
+y_1 = 1 / (x**2 + 1)
+y_2 = 2 / (x**2 + 1)
+y_3 = 3 / (x**2 + 1)
+
+plt.title("Functii")
+plt.xlabel("$x$")
+plt.ylabel("$y$")
+
+plt.plot(x, y_1, label = "$\\frac{1}{x^2 + 1}$")
+plt.plot(x, y_2, label = "$\\frac{2}{x^2 + 1}$")
+plt.plot(x, y_3, label = "$\\frac{3}{x^2 + 1}$")
+
+
+plt.legend()
+plt.axhline(0, color="black", linewidth=0.8)
+plt.axvline(0, color="black", linewidth=0.8)
+plt.show()
+
+#6 
+
+
+x = np.linspace(-4.0,3,100)
+y_1 = x**2 + 2*x
+y_2 = 2*x + 3
+x_int = np.array([-np.sqrt(3),np.sqrt(3)])
+y_int = 2*x_int + 3
+plt.scatter(x_int,y_int, s = 20)
+
+plt.title("Functii")
+plt.xlabel("$x$")
+plt.ylabel("$y$")
+
+plt.plot(x, y_1, label = "$x^2+2x$")
+plt.plot(x, y_2, label = "$2x+3$")
+
+plt.legend()
+plt.axhline(0, color="black", linewidth=0.8)
+plt.axvline(0, color="black", linewidth=0.8)
+plt.show()
+
+#7
+
+x = np.linspace(-1.5,1.5,100)
+y_1 = x
+y_2 = x**2
+y_3 = x**4
+y_4 = x**6
+
+plt.title("Functii")
+plt.xlabel("$x$")
+plt.ylabel("$y$")
+
+plt.plot(x, y_1, label = "$x$") #nu e para
+plt.plot(x, y_2, label = "$x^2$")
+plt.plot(x, y_3, label = "$x^4$")
+plt.plot(x, y_3, label = "$x^6$")
+
+plt.legend()
+plt.axhline(0, color="black", linewidth=0.8)
+plt.axvline(0, color="black", linewidth=0.8)
+plt.show()
+
+#8
+
+x = np.linspace(-2,2)
+y = np.linspace(-2,2)
+X, Y = np.meshgrid(x,y)
+Z = X * np.exp(-(X**2 + Y**2))
+
+fig = plt.figure()
+ax = fig.add_subplot(111, projection="3d")
+ax.plot_surface(X,Y,Z, alpha=0.85)
+
+ax.set_title("$f(x,y) = e^{-(x^2+y^2)}$")
+ax.set_xlabel("$x$")
+ax.set_ylabel("$y$")
+ax.set_zlabel("$z$")
+plt.show()
+
+#9
+
+x = np.linspace(-2.4,2.4)
+y = np.linspace(-2.4,2.4)
+X, Y = np.meshgrid(x,y)
+Z = X**2 + Y**2
+Z_4 = Z*0 +4
+
+fig = plt.figure()
+ax = fig.add_subplot(111, projection="3d")
+ax.plot_surface(X,Y,Z, alpha=0.5)
+ax.plot_surface(X,Y,Z_4, alpha=0.8)
+ax.view_init(elev=5, azim=19)
+
+ax.set_title("$f(x,y) = x^2 +y^2$")
+ax.set_xlabel("$x$")
+ax.set_ylabel("$y$")
+ax.set_zlabel("$z$")
+plt.show()
+