Which of the following statements is correct?

Note: only one of them is correct.

Question

Which of the following statements is correct?

Note: only one of them is correct.

BlackTom AI · Accepted Answer

The question asks which statement among the three options is correct, noting that only one is correct.
Option 1: 'Some of the three application examples converge and some diverge.' This claims a mix of outcomes across the three integrals. If the provided correct answer is that all converge, this option contradicts that by asserting variability in convergence. The reasoning flaw here is treating the set as heterogeneous without evidence; unless distribution of convergence is specified, you cannot assert both outcomes.
Option 2: 'All of the three of the application integrals DIVERGE.' This asserts universal divergence. If the established correct option states convergence for all three, this is directly opposite and therefore false. The error lies in assuming no integral converges, which would require a divergence analysis that contradicts the given information about convergence.
Option 3: 'All of the three application integrals CONVERGE.' This is the statement identified as correct. The justification relies on the premise or prior information that each of the three integrals satisfies the convergence criteria in their respective contexts. Recognizing that each integral meets the necessary convergence conditions avoids mislabeling any as divergent or conditional, and aligns with the claim that all converge.
In summary, the first option presents an unfounded mixed outcome, the second option claims universal divergence contrary to the given, and the third option aligns with the provided correct assertion that all three integrals converge. The key distinction is understanding whether convergence criteria apply uniformly across all three cases or not, and here they do for option 3.

MAT136 - Calculus 2 - Winter 2025 Week 6 Tutorial Submission

Which of the following statements is correct? Note: only one of them is correct.

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