limits
by parcadei
Context management for Claude Code. Hooks maintain state via ledgers and handoffs. MCP execution without context pollution. Agent orchestration with isolated context windows.
Run in ManusUse Cases
MCP Server Integration
AI tool integration using Model Context Protocol. Using limits.
API Integration
Easily build API integrations with external services.
Data Synchronization
Automatically sync data between multiple systems.
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
-
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 diffon 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.
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