Calculus II · Unit 4A · answer key
Unit 4A Practice Exam A Answer Key
Review complete answers and reasoning for Unit 4A Practice Exam A, including theorem choice and error justification.
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Review complete answers and reasoning for Unit 4A Practice Exam A, including theorem choice and error justification.
A complete series argument includes hypotheses, a named theorem or comparison, its conclusion, and any requested sum or error estimate.
Identify the object and structure before computing, then use answer reveals only after recording a complete justification.
Reading the key before choosing a test or treating a missing hypothesis as a minor presentation issue.
Unit 4A Practice Exam A Answer Key
Finish an honest attempt first. Then compare one numbered response at a time, locate the first line where your reasoning diverged, and retry without the key open.
Problem 1
.
Problem 2
Yes, it converges to .
Problem 3
.
Problem 4
.
Problem 5
Terms approach , so it diverges.
Problem 6
Converges because .
Problem 7
Converges by comparison with .
Problem 8
Ratio with approaches ; converges.
Problem 9
Conditional convergence.
Problem 10
Ratio limit ; converges absolutely.
Problem 11
Root limit ; converges absolutely.
Problem 12
Require , so .
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