Concept quiz

Answer without a formula sheet, then check explanations in the lessons.

1. Can a function have a limit at a point where it is undefined? Give an example.
2. Why can a density be greater than 1 without violating probability rules?
3. Which two facts justify evaluating a definite integral through an antiderivative?
4. Why does a stationary point not establish a constrained minimum?
5. Which assumptions make a sign bracket evidence for a root?
6. Why can a smaller finite-difference step give a worse result?
7. Distinguish quadrature error, omitted tail mass and model error.

Calibration: yes, a removable hole; probabilities are integrals with units; continuity and F′=f suffice here; compare endpoints/corners and feasible candidates; continuity plus opposite signs; cancellation and rounding; respectively finite-interval approximation, excluded support and mismatch with reality. A memorized phrase without an example needs repair.