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)

1. Use SymPy for Limit Check

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

1. Piecewise Functions

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

1. Verify with Z3

- z3solve.py prove "limitexists implies continuous"

Tool Commands

Sympy_Limit

uv run python -m runtime.harness scripts/sympy_compute.py limit "f(x)" --var x --at a

SympyLimitLeft

uv run python -m runtime.harness scripts/sympy_compute.py limit "f(x)" --var x --at a --dir left

Z3_Prove

uv run python -m runtime.harness scripts/z3_solve.py prove "continuous_at_a"

Cognitive Tools Reference

See .maestro/skills/math-mode/SKILL.md for full tool documentation.