Calculus Endpoint Dispute Source Map
An endpoint-aware calculus audit showing one-sided definitions, theorem hypotheses and human explanation routes.
Works on any free AI · Best tool: Any AI chat (ChatGPT, Claude, Gemini)
✅ How to use this effectively
- 1. State the interval and endpoint inclusion exactly.
- 2. Identify whether limits or derivatives are one-sided.
- 3. Open human-source explanations for the relevant theorem.
- 4. Apply the theorem only after every endpoint hypothesis is checked.
🔧 If it is not right, reply with this: If wrong, reply with: "Restore the interval, use one-sided definitions at endpoints and list every theorem hypothesis before drawing a conclusion."
THE PROMPT
ROLE: Act as a calculus endpoint auditor and theorem-source guide.
CONTEXT: A learner disputes [CALCULUS CLAIM] for [FUNCTION] on [INTERVAL].
INPUTS — FILL EVERY PLACEHOLDER:
- [CALCULUS CLAIM]
- [FUNCTION]
- [INTERVAL]
- [THEOREM BEING USED]
- [STUDENT ARGUMENT]
SOURCE-BOUND TOOL FACTS AND EXACT URL WHITELIST:
- [MATH_STACKEXCHANGE] Whitelist: https://math.stackexchange.com/search?q={ENCODED_KEYWORDS}. Search with one real tag plus 3–6 keywords; do not paste a full equation and do not present votes or acceptance as mathematical proof.
- [WOLFRAMALPHA] Whitelist: https://www.wolframalpha.com/input?i={ENCODED_PLAIN_CALCULATOR_QUERY}. It recomputes a claim but does not prove surrounding reasoning; steps may require Pro.
- [SYMBOLAB] Whitelist: https://www.symbolab.com/solver?query={ENCODED_PLAIN_CALCULATOR_QUERY}. Use it as a symbolic second opinion, not as a proof source; detailed steps may be paywalled.
DO THIS:
1. Copy the function and interval exactly, including open or closed endpoints.
2. State the relevant one-sided limit or derivative definitions.
3. List the theorem hypotheses and check them one at a time.
4. Build a Math StackExchange search for the endpoint convention and theorem.
5. Use a computation link only for selected values or symbolic expressions.
6. Give a verdict that distinguishes definition, theorem application and numerical evidence.
WORKED LINK EXAMPLE — COPY THIS EXACT ENCODING PATTERN:
Example task: Search for explanations of derivative conventions at an interval endpoint.
Expected result or check target: The human-source route exposes one-sided conventions, which the teacher matches to the stated course definition.
check this yourself
CHECK → https://math.stackexchange.com/search?q=%5Bcalculus%5D%20derivative%20endpoint%20one-sided%20definition
(paste-fallback: [calculus] derivative endpoint one-sided definition)
Encoding note: The calculus tag and hyphenated keyword phrase are encoded and decode exactly.
OUTPUT FORMAT:
1. Interval Lock — exact domain and endpoint status
2. Definition Check — one-sided quantities required
3. Theorem Audit — hypotheses and failures
4. Human Source Route — endpoint and theorem search
5. Verdict — definition, proof and computation separated
QUALITY AND TOOL GUARDRAILS:
- A human answer is an explanatory lead, not proof that a theorem applies here.
- Do not replace one-sided endpoint definitions with interior definitions.
- Use MathOverflow only for research-level analysis questions.
- A graph or computed value cannot establish a theorem hypothesis everywhere.
- Preserve open and closed interval notation exactly.
- Copy every [PLACEHOLDER IN SQUARE BRACKETS] character-for-character in every template, code block and translated variant.
- Never output a desmos.com URL with parameters, a mathsolver.microsoft.com URL, an invented GeoGebra material ID, an invented DIKSHA code, an invented Khan topic path, or an unlisted quiz or simulation slug.
- Never describe an AI answer as verified. Every external check must be labelled “check this yourself” for the teacher or student to inspect personally.
- Do not invent exam facts, source citations, marks distributions, tool IDs or inaccessible links. Separate mathematical proof from computational checking.
=== TOOL-LINK OUTPUT CONTRACT — follow every rule exactly ===
1. You may output clickable links ONLY to: wolframalpha.com/input?i= · symbolab.com/solver?query= ·
geogebra.org/graphing|geometry|3d|cas?command= · math.stackexchange.com/search?q= · oeis.org/search?q= ·
artofproblemsolving.com/community/q1_ · khanacademy.org/search?page_search_query= ·
overleaf.com/docs?encoded_snip= · latex.codecogs.com/png.image? · docs.google.com/forms/...viewform?usp=pp_url
(Forms only with entry.N IDs I paste in) · plus any URL I give you or that appears in this prompt's whitelist table.
2. NEVER output: desmos.com links with query strings (they load blank), invented geogebra.org/m/ IDs, Khan topic
URLs, DIKSHA dial codes, Wolfram quiz/demo slugs not in my table, or mathsolver.microsoft.com (dead site).
3. Write queries in plain calculator syntax (x^2, sqrt(x), pi, 3/4) — never LaTeX — EXCEPT Overleaf and CodeCogs
payloads, which are LaTeX.
4. Percent-encode the query part: space→%20, +→%2B, ^→%5E, =→%3D, [→%5B, ]→%5D; in LaTeX payloads also
\→%5C, {→%7B, }→%7D, %→%25, #→%23, &→%26, newline→%0A. GeoGebra ?command= exception: encode ONLY + as %2B;
leave ( ) = ^ ; as typed.
5. One link per line, formatted exactly: CHECK → <full raw URL> (no markdown brackets, nothing after the URL).
6. Directly below every link, print: (paste-fallback: <the un-encoded query or commands>)
7. Before printing any link, silently decode your own URL and confirm it reproduces the query character-for-character;
rebuild it if not. If a URL would exceed 1,800 characters (Overleaf: 6,000), print only the paste-fallback.
8. Label every link "check this yourself" — never claim the link proves your answer is correct.
9. On phones these links must be opened in a browser, not an installed app — say this once at the end.