Provides step-by-step problem-solving strategies for limits in real analysis.
Install
mkdir -p .claude/skills/limits && curl -L -o skill.zip "https://agentskills.codes/api/skills/download/4580" && unzip -o skill.zip -d .claude/skills/limits && rm skill.zipInstalls to .claude/skills/limits
Activation
This is the description your AI agent reads to decide when to run this skill — the better it matches your request, the more reliably it fires.
Problem-solving strategies for limits in real analysisKey capabilities
- →Perform direct substitution
- →Apply L'Hopital's rule
- →Verify bounds with Squeeze Theorem
- →Execute epsilon-delta proofs
How it works
It follows a decision tree of mathematical strategies, using symbolic computation and logical solvers to verify results.
Inputs & outputs
When to use limits
- →Calculating limits using direct substitution
- →Applying L'Hopital's rule for indeterminate forms
- →Verifying epsilon-delta proofs
About this skill
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.
When not to use it
- →For non-mathematical problems
Limitations
- →Requires understanding of real analysis
- →Symbolic solvers may fail on complex expressions
How it compares
It provides a structured, algorithmic approach to solving limits compared to manual derivation.
Compared to similar skills
limits side by side with the closest alternatives in the catalog.
| Skill | Installs | Updated | Safety | Difficulty |
|---|---|---|---|---|
| limits (this skill) | 1 | 7mo | Review | Advanced |
| literature-review | 559 | 2mo | Review | Advanced |
| openalex-database | 48 | 7mo | Review | Intermediate |
| scientific-critical-thinking | 18 | 7mo | Review | Advanced |
Try saying
Example prompts that trigger this skill in your AI assistant.
More by parcadei
View all by parcadei →You might also like
literature-review
K-Dense-AI
Conduct comprehensive, systematic literature reviews using multiple academic databases (PubMed, arXiv, bioRxiv, Semantic Scholar, etc.). This skill should be used when conducting systematic literature reviews, meta-analyses, research synthesis, or comprehensive literature searches across biomedical, scientific, and technical domains. Creates professionally formatted markdown documents and PDFs with verified citations in multiple citation styles (APA, Nature, Vancouver, etc.).
openalex-database
davila7
Query and analyze scholarly literature using the OpenAlex database. This skill should be used when searching for academic papers, analyzing research trends, finding works by authors or institutions, tracking citations, discovering open access publications, or conducting bibliometric analysis across 240M+ scholarly works. Use for literature searches, research output analysis, citation analysis, and academic database queries.
scientific-critical-thinking
davila7
Evaluate research rigor. Assess methodology, experimental design, statistical validity, biases, confounding, evidence quality (GRADE, Cochrane ROB), for critical analysis of scientific claims.
biorxiv-database
lifangda
Efficient database search tool for bioRxiv preprint server. Use this skill when searching for life sciences preprints by keywords, authors, date ranges, or categories, retrieving paper metadata, downloading PDFs, or conducting literature reviews.
physics-validator
omriwen
Validate optical physics parameters including Fresnel numbers, diffraction regimes, and resolution limits. This skill should be used when configuring Telescope, Microscope, or Camera instruments to ensure physically realistic parameters.
fda-database
davila7
Query openFDA API for drugs, devices, adverse events, recalls, regulatory submissions (510k, PMA), substance identification (UNII), for FDA regulatory data analysis and safety research.