Calculus II · Unit 4B · answer key
Unit 4B Practice Exam B Answer Key
Review complete answers and reasoning for Unit 4B Practice Exam B, including theorem choice and error justification.
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Review complete answers and reasoning for Unit 4B Practice Exam B, including theorem choice and error justification.
A complete solution preserves the series identity, interval, endpoint logic, and approximation claim as one chain.
Write the objective and conditions first, solve independently, then use one answer reveal to repair the earliest incorrect decision.
Checking algebra while leaving the convergence domain or error certification unstated.
Unit 4B Practice Exam B 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
Radius ; at , terms are and diverge; at , terms are and do not approach zero. Interval .
Problem 2
, .
Problem 3
Substitute , differentiate, and obtain .
Problem 4
.
Problem 5
.
Problem 6
.
Problem 7
Four nonzero terms suffice: through . The first omitted magnitude is , and the terms decrease.
Problem 8
Using three nonzero terms,
Problem 9
Recurrence gives , so .
Problem 10
Uniform convergence uses one index working simultaneously for all points.
Problem 11
Small-angle pendulum: replace by .
Problem 12
Answers vary but must name a valid remainder estimate and verify its hypotheses.
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