Vibecosystem limits

Problem-solving strategies for limits in real analysis

install

source · Clone the upstream repo

git clone https://github.com/vibeeval/vibecosystem

Claude Code · Install into ~/.claude/skills/

T=$(mktemp -d) && git clone --depth=1 https://github.com/vibeeval/vibecosystem "$T" && mkdir -p ~/.claude/skills && cp -r "$T/skills/math/real-analysis/limits" ~/.claude/skills/vibeeval-vibecosystem-limits && rm -rf "$T"

manifest: skills/math/real-analysis/limits/SKILL.md

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.