Calculus I · Unit 2B · quiz

Approximation Concept Quiz

Concept Quiz: Approximation

• Why is a tangent line a good local approximation? • How should the base point for a linearization be chosen? • Distinguish $dy$ from $\Delta y$ . • What is the difference between absolute and relative error? • Derive Newton's update from a tangent equation. • Name two reasons Newton's method can fail.

After the explanation

Use the section idea

Reading lens

A differentiable curve behaves like its tangent line over a small enough neighborhood, with concavity explaining the direction of error.

Mental model

Linearization, differentials, and Newton's method reuse one local line for estimation, uncertainty, or a better root guess.

Decision

Choose a nearby easy input, record the local slope, and state why the requested change is small enough for the model.

Common trap

Presenting a tangent estimate as exact or running Newton iterations without checking residuals and failure modes.

Check yourself

Can you give the estimate, error direction, units, and a reason the local line is trustworthy here?

Structured concept quiz

Approximation Concept Quiz

Write a response before revealing the model. These conceptual items use an honest attempt-and-reveal rubric rather than pretending an open response has one machine-provable wording.

Interactive checkapproximation-concept-quiz-01

Why is a tangent line a good local approximation?