numpy as np import matplotlib.pyplot as plt

Create data for the graph

x = np.linspace(1, 100, 500) y = np.full_like(x, 4)

Plot the graph

plt.figure(figsize=(8, 6)) plt.plot(x, y, label="y = 4", color='blue') plt.axhline(y=4, color='red', linestyle='--', label='Limit as x -> infinity = 4') plt.xlabel('x') plt.ylabel('y') plt.title('Graph Showing the Limit as x Approaches Infinity = 4') plt.legend() plt.grid() plt.show()Here is the graph illustrating that as $x$ approaches infinity, the value of $y$ approaches 4. The horizontal dashed red line represents the limit $y = 4$.

Do you want any details or have further questions?

Related Questions:

1. What are other ways to represent this limit mathematically?
2. How does this compare to limits where $x$ approaches a finite value?
3. What happens if the limit changes with $x$, e.g., $\lim_{{x \to \infty}} (1/x)$?
4. Can we explore functions whose limits do not exist as $x \to \infty$?
5. How is this limit useful in real-world scenarios or calculus problems?

Tip:

Always look for horizontal asymptotes when evaluating the behavior of functions as $x \to \infty$.