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Limits · vibeeval | DecimalAI

scienceby vibeeval

Limits

vibeeval/limits

Source vibeeval/vibecosystem ↗License MIT

Problem-solving strategies for limits in real analysis

SkillScore95Maintained

Automatic

Tutoring & Education pack

Last verified 8/3/2026

What it changes

Passed 21 of 22 test cases with the skill, and 12 of 22 without it.

Without skill55%

With skill95%

Checks it passed that the model alone missed

Finds delta in terms of epsilon
Passes oo or inf to the --at flag in sympy_compute.py limit
Uses scripts/sympy_compute.py diff to differentiate tan(x) - x

and 6 more in the full report

9 fixed12 passed either way1 still failing0 broke

Pass-rate lift: +41 pp
Tokens: -29%
Agent turns: 0%
Response time: -56%

Model gemini-3.6-flashMeasured 8/3/2026v121 of 22 cases passed with skill

Tokens, turns and time describe resource use, not a dollar price.

Use this skill

Save it into your project's skills folder. Claude Code picks it up in its next session.

curl -fsSL --create-dirs -o .claude/skills/vibeeval-limits/SKILL.md https://app.decimal.ai/s/vibeeval-limits/SKILL.md

Want it pinned and updatable? pip install "decimalai>=0.15", then decimalai skills add vibeeval-limits, and start Claude Code with claude --plugin-dir "$(git rev-parse --show-toplevel)/.agents"

1 · One-time — install the CLI (docs ↗)

pip install "decimalai>=0.15"

2 · Get the skill — writes .agents/skills/vibeeval-limits/ and pins it in .decimal/skills.lock

decimalai skills add vibeeval-limits

No CLI? Get the same file — curl · raw file

curl -fsSL --create-dirs -o .claude/skills/vibeeval-limits/SKILL.md https://app.decimal.ai/s/vibeeval-limits/SKILL.md

Raw file: /s/vibeeval-limits/SKILL.md ↗ · machine-readable summary at /s/vibeeval-limits.json ↗

Safety checks: 3 of 3 passed

Code scan CleanIntent PassedContent Clean

See it in action

One of 9 test cases the skill fixed. Same model, same prompt, with and without the skill.

1 of 9

Prompt

Write the full terminal command to calculate lim_{x->0} sin(x)/x using the project runtime harness.

What was checked, without and with the skill
Checked	Without skill	With skill
Executes uv run python -m runtime.harness scripts/sympy_compute.py limit "sin(x)/x" --var x --at 0	Missed	Passed

case-07 · gemini-3.6-flash · 8/3/2026 · answers are capped and redacted

What's inside

The instructions your model reads when the skill loads.

SKILL.md47 linessingle file

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

Track record

Benchmark

21 / 22

test cases passed, vs 12 / 22 without

Adoption

Users: 1
Times used: 4

Safety and source details

SkillSafety

✓ 3 of 3 passed

Code scan15 of 15 checks clean

0 critical · 0 warning · 0 info — scanner v4 — 8/1/2026

View 15 scanner checks

live_secretremote_code_executionreverse_shelldata_exfiltrationssrf_metadataagent_snoopinganti_refusaldestructive_commandsobfuscated_unicodeunicode_homoglyphopaque_blobsuspicious_urltool_overreachtrigger_abuseprompt_injection_phrasing

IntentSafe

LLM judge · does the skill do what it claims

ContentClean

LLM judge · policy & harmful-content review

Source

Imported

vibeeval / vibecosystem

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

View on GitHub ↗

License MITImported 8/1/2026Version v1

Other skills for the same job

Published skills whose descriptions closely match this one, with their headline benchmark lift.

vibeeval/convergenceProblem-solving strategies for convergence in real analysisClose match+32 pp pass-rate lift

More skills from the same source and nearby in the registry, with their headline benchmark lift.

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See it in action

What's inside

Limits

When to Use

Decision Tree

Tool Commands

Sympy_Limit

Sympy_Diff

Z3_Prove

Track record

Benchmark

Adoption

SkillSafety

Source

Other skills for the same job

Related skills