Update app.py

app.py

@@ -147,6 +147,35 @@ NOTE: For eigenvalue problems, use 'lam = Symbol('lam')' instead of importing fr
      ```
    - For systems of equations that might be linearly dependent, use row reduction instead of matrix inversion. Here's the template for handling such systems:
 
+7. Limit Calculations:
+   - ALWAYS compute one-sided limits (from the left and the right) when evaluating any limit:
+     ```python
+     # Example:
+     x = Symbol('x')
+     expr = (sin(x)*cos(x) - x + x**3) / (x**3 * sqrt(1 + x) - x**3)
+     
+     # Calculate the limit from the left (x -> 0-):
+     left_limit = limit(expr, x, 0, dir='-')
+     print("Limit from the left (x -> 0-):")
+     print(left_limit)
+     
+     # Calculate the limit from the right (x -> 0+):
+     right_limit = limit(expr, x, 0, dir='+')
+     print("Limit from the right (x -> 0+):")
+     print(right_limit)
+     ```
+   - After computing both one-sided limits, verify if they match:
+     ```python
+     if left_limit == right_limit:
+         print("The two-sided limit exists and is:", left_limit)
+     else:
+         print("The two-sided limit does not exist.")
+     ```
+   - If the limit diverges (\(\infty\) or \(-\infty\)), explicitly state that in the print output.
+   - For piecewise or discontinuous functions, compute limits at all points of interest, including boundaries.
+
+   - **Important Note**: Always test limits symbolically first. If SymPy produces unexpected results, simplify the expression or expand it (e.g., using `series`) before re-evaluating the limit.
+   
 ```python
 from sympy import Matrix, symbols, solve