Calculus II · Unit 4B · review

Taylor Series Review

Exercise

Find $P_4$ for $\cos x$ at zero.

Exercise

Find $P_3$ for $\ln x$ at $a=1$ .

Exercise

Use a Taylor polynomial to approximate $e^{0.2}$ .

Exercise

Bound the approximation error.

Exercise

Derive the series for $\arctan x$ .

Exercise

Explain the distinction between a Taylor series and the function it is built from.

After the explanation

Use the section idea

Reading lens

Mixed work tests recognition: classify the task before selecting a convergence, construction, transformation, or error method.

Mental model

A complete solution preserves the series identity, interval, endpoint logic, and approximation claim as one chain.

Decision

Write the objective and conditions first, solve independently, then use one answer reveal to repair the earliest incorrect decision.

Common trap

Checking algebra while leaving the convergence domain or error certification unstated.

Check yourself

Can you reproduce the method and domain without the key?

Source & rights

Original instruction with traceable references.

BetterGrades-original; no direct adaptation declared in the verified handoff.

Reference textbooks remain rights-separated and are not published as application assets. Any direct adaptation requires separate identification and attribution.