Calculus 1 problems: functions, integrals, series

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The discussion revolves around solving older calculus exam problems without provided solutions. Participants are encouraged to verify their answers independently, particularly for questions involving differential equations and series convergence. The Ratio Test is recommended for determining the interval of convergence for series. The complexity of the questions is noted, as they typically offer three reasonable answer choices rather than simple True/False options. Engaging with the material and attempting to solve the problems is emphasized for better understanding.
BigBowler
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Mentor note: Moved from technical section, so is missing the homework template.
Im doing some older exams that my professor has provided, but I haven't got the solutions for these. Can someone help confirm that the solutions I've arrived at are correct?

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For these problems, it's probably better if you take a stab at checking them for yourself. For the first question, could the answer be B or C? For the second question, test each given function to see if it's a solution of the diff. equation. For the third and fourth questions, I would use the Ratio Test to determine the interval on which each series converges.
 
Thanks for the tips.
 
The questions are slightly more involved than True/False questions, as they really have only three reasonable answers. If you give a D response (Don't know), that's saying to the instructor that you really don't have a clue.
 

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