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limits

Problem-solving strategies for limits in real analysis

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This page reorganizes the original catalog entry around fit, installability, and workflow context first. The original raw source lives below.

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3,611

Hot score

Updated

March 20, 2026

Overall rating

C4.8

Composite score

4.8

Best-practice grade

B81.2

Install command

npx @skill-hub/cli install parcadei-continuous-claude-v3-limits

Repository

parcadei/Continuous-Claude-v3

Skill path: .claude/skills/math/real-analysis/limits

Problem-solving strategies for limits in real analysis

Open repository

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Primary workflow: Ship Full Stack.

Technical facets: Full Stack.

Target audience: everyone.

License: Unknown.

Original source

Catalog source: SkillHub Club.

Repository owner: parcadei.

This is still a mirrored public skill entry. Review the repository before installing into production workflows.

What it helps with

Install limits into Claude Code, Codex CLI, Gemini CLI, or OpenCode workflows
Review https://github.com/parcadei/Continuous-Claude-v3 before adding limits to shared team environments
Use limits for development workflows

Works across

Claude CodeCodex CLIGemini CLIOpenCode

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Sub-skills: 0.

Aggregator: No.

Original source / Raw SKILL.md

---
name: limits
description: "Problem-solving strategies for limits in real analysis"
allowed-tools: [Bash, Read]
---

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

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

### Z3_Prove
```bash
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.