limits

Problem-solving strategies for limits in real analysis

422 stars

Best use case

limits is best used when you need a repeatable AI agent workflow instead of a one-off prompt.

Problem-solving strategies for limits in real analysis

Teams using limits should expect a more consistent output, faster repeated execution, less prompt rewriting.

When to use this skill

  • You want a reusable workflow that can be run more than once with consistent structure.

When not to use this skill

  • You only need a quick one-off answer and do not need a reusable workflow.
  • You cannot install or maintain the underlying files, dependencies, or repository context.

Installation

Claude Code / Cursor / Codex

$curl -o ~/.claude/skills/limits/SKILL.md --create-dirs "https://raw.githubusercontent.com/vibeeval/vibecosystem/main/skills/math/real-analysis/limits/SKILL.md"

Manual Installation

  1. Download SKILL.md from GitHub
  2. Place it in .claude/skills/limits/SKILL.md inside your project
  3. Restart your AI agent — it will auto-discover the skill

How limits Compares

Feature / AgentlimitsStandard Approach
Platform SupportNot specifiedLimited / Varies
Context Awareness High Baseline
Installation ComplexityUnknownN/A

Frequently Asked Questions

What does this skill do?

Problem-solving strategies for limits in real analysis

Where can I find the source code?

You can find the source code on GitHub using the link provided at the top of the page.

SKILL.md Source

# 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.

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