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Limits

parcadei/limits

Problem-solving strategies for limits in real analysis

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on the repository, not the skill itself

Install

one command, takes just this skill from the repository 
npx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill limits

The instruction itself

8 sections, as written by the author

Limits

When to Use

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

Decision Tree

  • Direct Substitution
  • Try plugging in the value directly
  • If you get a determinate form, that's the answer
  • Indeterminate Form? (0/0, inf/inf)
  • Try algebraic manipulation (factor, rationalize)
  • Try L'Hopital's rule: sympy_compute.py diff on numerator/denominator
  • Squeeze Theorem
  • If bounded: find g(x) <= f(x) <= h(x) where lim g = lim h
  • Verify bounds with z3_solve.py prove
  • Epsilon-Delta Proof
  • For rigorous proof: set up |f(x) - L| < epsilon
  • Find delta in terms of epsilon
  • Verify with math_scratchpad.py verify

Tool Commands

Sympy_Limit

uv run python -m runtime.harness scripts/sympy_compute.py limit "sin(x)/x" --var x --at 0

Sympy_Diff

uv run python -m runtime.harness scripts/sympy_compute.py diff "x**2" --var x

Z3_Prove

uv run python -m runtime.harness scripts/z3_solve.py prove "limit_bound" --vars x

Cognitive Tools Reference

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

How to use it

Copy the folder

Take parcadei/limits from the repository into ~/.claude/skills for personal use, or into .claude/skills inside a project.

Check the name does not clash

The agent identifies a skill by the name field in its header. Two skills with the same name cannot sit side by side — one of them will be ignored.