limits code added

Author: ADIL8590

limits.py

@@ -0,0 +1,44 @@
+#finding  limits of a function using user defined function
+def find_limit(func, x, approach):
+    if approach == 'left':
+        return func(x - 0.0001)  # Approaching from the left
+    elif approach == 'right':
+        return func(x + 0.0001)  # Approaching from the right
+    else:
+        raise ValueError("Approach must be 'left' or 'right'.")
+
+
+# Example usage:
+if __name__ == "__main__":
+    # Define a sample function
+    def function(x):
+        return (x**3 - 1) / (x - 1)
+
+    x_value = 1
+    left_limit = find_limit(function, x_value, 'left')
+    right_limit = find_limit(function, x_value, 'right')
+
+    
+
+
+    print(f"Left-hand limit as x approaches {x_value}: {left_limit}")
+    print(f"Right-hand limit as x approaches {x_value}: {right_limit}")
+    if abs(left_limit - right_limit) < 0.1:
+        print(f"The limit as x approaches {x_value} is equal to: {int(right_limit)}")
+    else:
+        print(f"The limit does not exist as the left-hand limit ({left_limit}) and right-hand limit ({right_limit}) are not equal.Hence limit does not exist.")
+
+
+#plot function to visualize limits  
+import numpy as np
+import matplotlib.pyplot as plt
+x_vals = np.linspace(0.5, 1.5, 100)
+y_vals = [function(x) for x in x_vals]
+plt.plot(x_vals, y_vals, label='f(x)')
+plt.axvline(x=x_value, color='red', linestyle='--', label=f'x = {x_value}')
+plt.xlabel('x')
+plt.ylabel('f(x)')
+plt.title('Function Visualization')
+plt.legend()
+plt.grid(True)
+plt.show()