Let A1- A2- A3 be regions in the xy-plane defined by A1-x- y-x2-2y2 - 1- A2-x- y-x-3-2-2-y-3- 1- A3-x- y- max-x- -2-y- 1- Then-

The correct option is A A_3 ⊂ A_1 ⊂ A_2 From the figure, A_3⊂ A_1⊂ A_2 ...

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Family of Planes Passing through the Intersection of Two Planes

Let A1, A2,...

Question

Let $A_{1}, A_{2}, A_{3}$ be regions in the xy-plane defined by $A_{1} = {(x, y) : x^{2} + 2 y^{2} \leq 1}$ , $A_{2} = {(x, y) : | x |^{3} + 2 \sqrt{2} | y |^{3} \leq 1}$ , $A_{3} = {(x, y) : m a x (| x |, \sqrt{2} | y |) \leq 1}$ . Then.

A_{1} \supset A_{2} \supset A_{3}

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A_{3} \subset A_{1} \subset A_{2}

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A_{2} \supset A_{3} \supset A_{1}

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A_{3} \subset A_{2} \subset A_{1}

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A_{1}, A_{2},

A_{3}

R^{2}

A_{1} = {(x, y) : x \geq 0, y \geq 0, 2 x + 2 y - x^{2} - y^{2} > 1 > x + y}, A_{2} = {(x, y) : x \geq 0, y \geq 0, x + y > 1 > x^{2} + y^{2}}, A_{3} = {(x, y) : x \geq 0, y \geq 0, x + y > 1 > x^{3} + y^{3}} .

| A_{1} |, | A_{2} |,

| A_{3} |

A_{1}, A_{2}

A_{3}

\frac{a_{1}}{a_{1}} + \frac{a_{2}}{a_{2}} + \frac{a_{3}}{a_{3}} + \dots \frac{a_{n}}{a_{n}} = \frac{1}{1} + \frac{1}{a_{1}} + \frac{a_{1}}{a_{2}} + \frac{a_{2}}{a_{3}} + \dots \frac{a_{n - 2}}{a_{n - 1}}

a_{1}, a_{2}, a_{3} \in + R

\frac{a_{1}}{a_{2}} + \frac{a_{2}}{a_{3}} + \frac{a_{3}}{a_{1}} \geq 3

a_{1}, a_{2}, a_{3}, a_{4}, a_{5} > 0

\frac{a_{1}}{a_{2} + a_{3}} + \frac{a_{2}}{a_{3} + a_{4}} + \frac{a_{3}}{a_{4} + a_{5}} + \frac{a_{4}}{a_{5} + a_{1}} + \frac{a_{5}}{a_{1} + a_{2}} \geq \frac{5}{2}

a_{1}, a_{2}, a_{3}, . . . . . a_{n}

\frac{a_{1}}{a_{2} + a_{3} + . . . a_{n}}, \frac{a_{2}}{a_{1} + a_{3} + . . . . + a_{n}}, \frac{a_{n}}{a_{1} + a_{2} + . . . + a_{n - 1}}

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