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limits

Problem-solving strategies for limits in real analysis

Stars
3,795
Source
parcadei/Continuous-Claude-v3
Updated
2026-01-26
Slug
parcadei--Continuous-Claude-v3--limits
View on GitHubRaw SKILL.md

// install — copy + paste into any project

mkdir -p .claude/skills && curl -fsSL https://raw.githubusercontent.com/parcadei/Continuous-Claude-v3/HEAD/.claude/skills/math/real-analysis/limits/SKILL.md -o .claude/skills/limits.md

Drops the SKILL.md into .claude/skills/limits.md. Works with Claude Code, Cursor, and any agent that loads SKILL.md files from .claude/skills/.

Limits

When to Use

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

Decision Tree

  1. Direct Substitution

    • Try plugging in the value directly
    • If you get a determinate form, that's the answer

  2. Indeterminate Form? (0/0, inf/inf)

    • Try algebraic manipulation (factor, rationalize)
    • Try L'Hopital's rule: sympy_compute.py diff on numerator/denominator

  3. Squeeze Theorem

    • If bounded: find g(x) <= f(x) <= h(x) where lim g = lim h
    • Verify bounds with z3_solve.py prove

  4. 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.