limits
Problem-solving strategies for limits in real analysis
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技能内容
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 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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原文件路径
.claude/skills/math/real-analysis/limits/SKILL.md