Calculus II · Unit 4A · diagnostic

Unit 4A Prerequisite Diagnostic

Before beginning, verify that you can simplify rational expressions, work with exponentials and logarithms, evaluate improper integrals, and use basic limits at infinity.

Exercise

Evaluate $\lim_{n\to\infty}(4n^2+1)/(2n^2-3)$ .

Exercise

Simplify $(n+1)!/n!$ .

Exercise

Evaluate $\int_1^\infty x^{-2}\,dx$ .

Exercise

Solve $|r|<1$ for $r=(x-2)/3$ .

Exercise

State whether $\ln n/n\to0$ .

Exercise

Expand the first four terms of $(1+x)^4$ .

After the explanation

Use the section idea

Reading lens

Mixed work removes the method label; classify first, complete an honest attempt, then diagnose the earliest incorrect decision.

Mental model

A complete series argument includes hypotheses, a named theorem or comparison, its conclusion, and any requested sum or error estimate.

Decision

Identify the object and structure before computing, then use answer reveals only after recording a complete justification.

Common trap

Reading the key before choosing a test or treating a missing hypothesis as a minor presentation issue.

Check yourself

Can you reproduce the argument without the key and explain why a tempting alternative test is weaker?

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.