limits skill
Problem-solving strategies for limits in real analysis
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Install the limits skill
A skill is a folder. Copy it into your agent's skills folder and the agent loads it when the task matches its description.
git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3.git /tmp/Continuous-Claude-v3 mkdir -p ~/.claude/skills cp -r /tmp/Continuous-Claude-v3/.claude/skills/math/real-analysis/limits ~/.claude/skills/limits
available in every project
In the Claude apps, zip the folder and upload it from the Skills settings. The folder on GitHub
The instructions your agent would load
SKILL.md as published, without the frontmatter. Read it on GitHub
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 0Sympy_Diff
uv run python -m runtime.harness scripts/sympy_compute.py diff "x**2" --var xZ3_Prove
uv run python -m runtime.harness scripts/z3_solve.py prove "limit_bound" --vars xCognitive Tools Reference
See .claude/skills/math-mode/SKILL.md for full tool documentation.
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