Maximum value of A1/A2

Calculus Level 4

Let \(a\) and \(b\) be two positive real numbers such that \( a+2b\le 1 \). Let \( A_1\) and \( A_2\) be, repectively, the areas of circles with radii \(ab^3\) and \( b^2\). What is the maximum possible value of \( \dfrac{A_1}{A_2}\)?

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