Calculus II · Unit 4B · practice

Unit 4B Mixed Practice

Practice method

Work in three passes

First, classify. Name the derivative idea or rule before writing algebra. This separates a recognition error from a calculation error.

Second, solve without the key. Record a complete attempt, including bounds, constants, domains, units, or interpretation when the prompt asks for them.

Third, reveal one answer at a time. Compare the first line where your work differs, close the answer, and redo that item from a blank start.

Unit 4B Mixed Practice

Exercise

Find the interval of convergence of $\sum n(x+1)^n/4^n$ .

Exercise

Find a series for $1/(1+9x^2)$ .

Exercise

Find the Maclaurin series for $x\sin x$ .

Exercise

Approximate $\int_0^{0.3}e^{-x^2}dx$ .

Exercise

Bound the error in $\cos(0.5)\approx1-0.5^2/2$ .

Exercise

Use coefficient matching for $y"=xy$ through four coefficients.

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.