Question 1

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Given the set

A equals open curly brackets open parentheses x comma y close parentheses element of real numbers squared colon space x squared plus y squared equals r subscript n superscript 2 comma space r subscript n equals fraction numerator 1 over denominator 2 end fraction open square brackets 3 plus left parenthesis negative 1 right parenthesis to the power of n open parentheses 2 minus fraction numerator ln open parentheses n to the power of 9 end exponent plus 1 close parentheses over denominator n end fraction close parentheses close square brackets comma space space for all n element of natural numbers close curly brackets
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