Correct answer: (A) S is not compact.; (D) S is not connected.
Explanation
Points (n+1/n,0) belong to S and escape to infinity, so S is unbounded and not compact. Circles n=1,2 have x≤2.5; every circle n≥3 has x≥3−1/3=8/3. The vertical line x=2.6 therefore separates two nonempty relatively open subsets of S. Hence it is disconnected. **A,D**.
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