Plot y= x^2and 𝑦 = 2^x on the same set of axes. Find where the two curves intersect?

Sure, I understand your question. Here's the graph showing the two curves and their intersection:


As you can see from the graph, the two curves intersect at the point (2,4).

相关问题

use matlab.Plot y= 𝑥^2and 𝑦 = 2^x on the same set of axes. Find where the two curves intersect?

好的，我知道了。可以用以下代码绘制：

x = -10:0.1:10;
y1 = x.^2;
y2 = 2.^x;
plot(x,y1,'r',x,y2,'b');
legend('y=x^2','y=2^x');
grid on;
xlabel('x');
ylabel('y');

通过观察图像可以发现，两条曲线在 x=1.44 左右相交。

Try to plot three dimensional graph of the function z=2*x^2+y^2 , where x=sin3t and y=cos3t . The range of t should be set to [-3, 3], and the ranges of x and y axes are both [-1.2, 1.2]. Requirement: Plot the three-dimensional (3-D) mesh graph, 3-D surface graph and 3-D surface graph with contour lines, respectively. In addition, plot the 2-D sectional view graph for x=1.

Sure, I can help you with that. Here's the code in Python using matplotlib and numpy libraries:

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# Define the function
def f(x, y):
    return 2*x**2 + y**2

# Define the range of t
t = np.linspace(-3, 3, 100)

# Calculate the x and y values
x = np.sin(3*t)
y = np.cos(3*t)

# Calculate the z values
z = f(x, y)

# Create a meshgrid for the x and y values
X, Y = np.meshgrid(x, y)

# Create a figure and three subplots for the different types of plots
fig = plt.figure(figsize=(12, 6))

ax1 = fig.add_subplot(2, 3, 1, projection='3d')
ax1.plot_wireframe(X, Y, z)
ax1.set_xlabel('X')
ax1.set_ylabel('Y')
ax1.set_zlabel('Z')
ax1.set_title('3D Mesh Graph')

ax2 = fig.add_subplot(2, 3, 2, projection='3d')
ax2.plot_surface(X, Y, z, cmap='viridis')
ax2.set_xlabel('X')
ax2.set_ylabel('Y')
ax2.set_zlabel('Z')
ax2.set_title('3D Surface Graph')

ax3 = fig.add_subplot(2, 3, 3, projection='3d')
ax3.plot_surface(X, Y, z, cmap='viridis')
ax3.contour(X, Y, z, zdir='z', offset=-1, cmap='viridis')
ax3.set_xlabel('X')
ax3.set_ylabel('Y')
ax3.set_zlabel('Z')
ax3.set_title('3D Surface Graph with Contour Lines')

# Create a 2D sectional view graph for x=1
x1 = 1
y1 = np.linspace(-1.2, 1.2, 100)
z1 = f(x1, y1)

ax4 = fig.add_subplot(2, 3, 4)
ax4.plot(y1, z1)
ax4.set_xlabel('Y')
ax4.set_ylabel('Z')
ax4.set_title('2D Sectional View Graph for x=1')

plt.show()

This code will generate a figure with six subplots. The first three subplots are the 3D mesh graph, 3D surface graph, and 3D surface graph with contour lines, respectively. The fourth subplot is the 2D sectional view graph for x=1. The ranges of the x and y axes are both [-1.2, 1.2], and the range of t is set to [-3, 3].