MATH U101 · Doubt clinic · index
Doubts, worked from zero
One card per doubt you send, filed on a topic page that matches the notes. Two cards so far, both Module 2 (Tutorial 4, 13 Sep).
Every doubt you send gets one card: the question as set, where the idea lives in the notes, the explanation rebuilt from first principles with the picture drawn, the mistake the question is designed to catch, and a twin to try with the card closed. Cards live on topic pages — one page per idea, matching the notes — so revising a topic means one page, not a hunt. The table below lists every card; filter it by topic, module or the date you sent it.
Topic pages
All cards
| Card | The question, in one line | Topic page | Source | Filed |
|---|---|---|---|---|
| Osculating circle of y = x² at x = 1 | What the circle is, why its radius is 1/κ and its centre P + ρN, which side, and how to write the parametrization. | Curvature, T and N | Tutorial 4 Q3 | 13 Sep |
| Where an ellipse bends most | Show κ is largest on the major axis and smallest on the minor: what a finished "show that" looks like. | Curvature, T and N | Tutorial 4 Q4 | 13 Sep |
What the two cards share
- Curvature questions are recipe questions. Parametrise → v, |v| → T → dT/dt → κ, N — or a shortcut formula (graph / parametric) when the curve's form allows. Decide the route in the first line.
- The identity sin² + cos² = 1 does the heavy lifting in both: it collapsed |⟨−4, 2⟩| and it made the ellipse's numerator constant. Expect it.
- Audit every geometric answer with one distance or one special case: centre-to-point = ρ; a = b gives the circle.
"Thomas' Calculus 15th ed. §13.4 only. Give me the osculating circle of y = x³ at x = 1 one step at a time — stop after each step so I can try the next." · "Using κ = |x′y″ − y′x″|/(x′² + y′²)3/2, check my claim that x = 3 cos t, y = 2 sin t has κmax = 3/4 and κmin = 2/9, and tell me where I'd lose marks." Stay clear of §13.5 (binormal, torsion) — not on the syllabus.