Continuity

When to Use

Use this skill when working on continuity problems in real analysis.

Decision Tree

1. Check Definition

   • f(a) exists (function defined at point)
   • lim_{x->a} f(x) exists
   • lim_{x->a} f(x) = f(a)

2. Use SymPy for Limit Check

   • sympy_compute.py limit "f(x)" --var x --at a
   • Compare with f(a)

3. Piecewise Functions

   • Check left and right limits separately
   • sympy_compute.py limit "f(x)" --var x --at a --dir left

4. Verify with Z3

   • z3_solve.py prove "limit_exists implies continuous"

Tool Commands

Sympy_Limit